拉丁矩阵问题：

现有N种不同形状的宝石，每种宝石有足够多颗。欲将这些宝石排列成m行n列的一个矩阵，m<=n,使矩阵中每一行和每一列的宝石都没有相同形状。试设计一个算法，计算出对于给定的m和n，有多少种不同的宝石排列方案。

算法设计:

对于给定的m和n，计算出不同的宝石排列方案数。

-Latin matrix problem: Existing N different shapes of stones, each gem has enough teeth. The stones are arranged in a matrix wishing m rows and n columns, m < = n, the matrix so that each row and each column do not have the same shape as the jewel. Try to design an algorithm to calculate for a given m and n, there are many different kinds of gems arranged plan. Algorithm Design: For a given m and n, the program calculates the number of different permutations gems.