Given an integer board_size, compute the number of distinct ways to place board_size queens on a board_size x board_size grid such that no two queens are in the same row, column, or diagonal.
Example 1
Input: 5
Output: 10
Explanation: There are 10 distinct ways to place 5 queens on a 5x5 board without conflicts.
Example 2
Input: 2
Output: 0
Explanation: No valid arrangement exists for 2 queens on a 2x2 board.
Constraints
Case 1
Input: 3
Expected: 0
Case 2
Input: 6
Expected: 4
Case 3
Input: 7
Expected: 40