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, write a program to return all distinct solutions to the n-queens puzzle.

Problem Note

Each solution contains a distinct board configuration of the n-queens' placement, where '1' and '0' both indicate a queen and an empty space respectively.

Example

Input: n = 4
Output:  
Solution 1  
[[ 0,  1,  0,  0],
 [ 0,  0,  0,  1],
 [ 1,  0,  0,  0],
 [ 0,  0,  1,  0]]

Solution 2
[[ 0,  1,  0,  0],
 [ 0,  0,  0,  1],
 [ 1,  0,  0,  0],
 [ 0,  0,  1,  0]]

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