Given an integer board_size, compute the total number of distinct ways to place board_size queens on a board_size x board_size grid such that no two queens threaten each other. Queens threaten each other if they share the same row, column, or diagonal. Return the count of valid arrangements.
Example 1
Input: 2
Output: 0
Explanation: No valid arrangement exists for 2x2 board.
Example 2
Input: 3
Output: 0
Explanation: No valid arrangement exists for 3x3 board.
Example 3
Input: 5
Output: 10
Explanation: There are 10 distinct valid arrangements for 5x5 board.
Constraints
Case 1
Input: 6
Expected: 4
Case 2
Input: 7
Expected: 40
Case 3
Input: 8
Expected: 92