在N*N的方格棋盘放置了N个皇后，使得它们不相互攻击（即任意2个皇后不允许处在同一排，同一列，也不允许处在与棋盘边框成45角的斜线上。

你的任务是，对于给定的N，求出有多少种合法的放置方法。 -Placed in the N* N the checkerboard N queen, so they don t attack each other (i.e. any two queen is not allowed in the same row, same column, are not allowed in and board frame 45 Angle diagonal lines.

Your task is to, for a given N, find out how many kinds of legal placement method.