N Rook Problem

Problem

Given the size of a chessboard and the number of rooks n, write a solution function that returns the number of ways to place n rooks on an n × n chessboard such that the following conditions are met:

Conditions:

• The n rooks cannot attack each other.
• No rook can be placed where the row number and column number are the same.

Reference:

• The N-Rook problem involves placing n rooks on an n × n chessboard such that no two rooks can attack each other.
• A rook can attack any other piece along its row or column.
• Generally, the number of ways to place n rooks on an n × n chessboard without any two rooks attacking each other is equal to $n!$.

Constraints

• n is a natural number between 2 and 10.

Test Case

Explanation for Test Case 1

• For a 2 × 2 chessboard, there is only one way to place 2 rooks such that the given conditions are satisfied.
  

Explanation for Test Case 2

• For a 3 × 3 chessboard, there are 2 ways to place 3 rooks such that the given conditions are satisfied.

Explanation for Test Case 3

• For a 5 × 5 chessboard, there are a total of 44 ways to place 5 rooks such that the given conditions are satisfied. One such arrangement is shown below: