Background



This a classical problem. N Queens are placed on a N x N checkerboard. There should not be more than one "Queen" on the same horizontal line, nor on the same vertical, nor on the same diagonal line.



Given the size of a checkerboard N, write a program to generate all possible solutions of placing N "Queens" on the board in ascending order.



eg. Given the size of the checkerboard is 4, the possible solutions of placing "Queens" is as follow:

2413

3142

The first solution of the example above is:

Place a "Queen" at 1st column 2nd row

Place a "Queen" at 2nd column 4th row

Place a "Queen" at 3rd column 1st row

Place a "Queen" at 4th column 3rd row

Since 2413 < 3142, the ouput is sorted in ascending order.

Input



Input contains an integer N (1 <= N <= 10), the size of the checkerboard.

Output



Output all possible solutions of the given checkerboard size in ascending order. If there is no solution for the given size of the checkerboard, output NIL.-Background



This is a classical problem. N Queens are placed on a N x N checkerboard. There should not be more than one "Queen" on the same horizontal line, nor on the same vertical, nor on the same diagonal line.



Given the size of a checkerboard N, write a program to generate all possible solutions of placing N "Queens" on the board in ascending order.



eg. Given the size of the checkerboard is 4, the possible solutions of placing "Queens" is as follow:

2413

3142

The first solution of the example above is:

Place a "Queen" at 1st column 2nd row

Place a "Queen" at 2nd column 4th row

Place a "Queen" at 3rd column 1st row

Place a "Queen" at 4th column 3rd row

Since 2413 < 3142, the ouput is sorted in ascending order.

Input



Input contains an integer N (1 <= N <= 10), the size of the checkerboard.

Output



Output all possible solutions of the given checkerboard size in ascending order. If there is no solution for the given size of the checkerboard, output NIL.