2133: All Latin Squares

## 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 ```