N-Queen

The N-Queen problem asks for placements of $N$ queens on an $N \times N$ chessboard in which no queen attacks another. A queen attacks every other queen in its row, in its column, and on its diagonals.

Given $N$, write a program that counts the placements of the $N$ queens. Placements that coincide after a rotation or a reflection are counted separately.

The first line contains $N$ ($1 \le N < 15$).

Print the number of placements of $N$ queens in which no queen attacks another.