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

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

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

Examples

Example 1

Input:  n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]

There exist two distinct solutions to the 4-queens puzzle as shown above.

Example 2

Input:  n = 1
Output: [["Q"]]

Constraints

• 1 <= n <= 9