2500: All Latin Squares
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题目描述
## Description
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.
## INPUT FORMAT
One line containing the integer N.
## SAMPLE INPUT
```
5
```
## OUTPUT FORMAT
A single integer telling the number of latin squares whose first row is 1 2 3 . . . N.
## SAMPLE OUTPUT
```
1344
```