N-Queens

Try to solve the N-Queens problem.

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Statement

The N-Queens puzzle is a classic problem in which the goal is to place n queens on an n ×\times n chessboard so that no two queens can attack each other.

In chess, a queen can move any number of squares horizontally, vertically, or diagonally. Therefore, no two queens can be placed in the same row, column, or diagonal.

Given an integer n, return all distinct valid arrangements of n queens on the board. Each arrangement should be represented as a list of strings, where each string corresponds to a row of the board. Within each string, 'Q' denotes a queen and '.' denotes an empty square.

Note: You can return the solutions in any order.

Constraints:

  • 1≤1 \leq n ≤9\leq 9

Examples

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