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

Sample Run
ENTER A WHOLE NUMBER (2-9): 4
THE NUMBER OF 4 x 4 LATIN
SQUARES IS 24.

What is the number of 5 x 5 Latin squares?

Source: 1993 USACO Qualifying Round 1