10541 - 拉丁正方形
一种正方形的数字编排 1 2 3 4 5 2 1 4 5 3 3 4 5 1 2 4 5 2 3 1 5 3 1 2 4 是一个55的拉丁正方形，每个1到5的整数在每行每列都出现且出现一次。 写个程序计算NN的的拉丁正方形的总数且要求第一行是： 1 2 3 4 5.......N 你的程序应该算称呼任意的从2到7的N(Your program should work for any N from 2 to 7)
Input
一行包含一个整数N
Output
只有一行没，表示拉丁正方形的个数，且拉丁正方形的第一行为 1 2 3 . . . N.
Examples
Input
5
Output
1344
Hint
All Latin Squares
A square arrangement of numbers
1 2 3 4 5 2 1 4 5 3 3 4 5 1 2 4 5 2 3 1 5 3 1 2 4
is a 5 x 5 Latin Square because each whole number from 1 to 5 appears once and only once in each row and column. Write a program that will compute the number of NxN Latin Squares whose first row is:
1 2 3 4 5.......N
Your program should work for any N from 2 to 7. PROGRAM NAME: latin INPUT FORMAT One line containing the integer N. SAMPLE INPUT (file latin.in) 5
OUTPUT FORMAT A single integer telling the number of latin squares whose first row is 1 2 3 . . . N. SAMPLE OUTPUT (file latin.out) 1344