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The n-queens puzzle is the problem of placing n queens on an n_×_n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.

For example,

There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..", // Solution 1
  "...Q",
  "Q...",
  "..Q."],


 ["..Q.", // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

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