N-Queens Problem

The N-Queens Problem is a classic puzzle involving placing N queens on an N x N chessboard such that no two queens threaten each other. This means no two queens can be in the same row, column, or diagonal.

Your task is to write a function n_queens(n: int) -> int that returns the number of distinct solutions to the N-Queens problem on an N x N chessboard.

Examples:

• If n = 4, there are 2 possible distinct solutions.
• If n = 1, the only possible solution is placing the queen on the single cell.

Here are some function calls to guide you:

print(n_queens(4))  # Output: 2
print(n_queens(1))  # Output: 1
print(n_queens(8))  # Output: 92

The challenge involves using concepts like backtracking to systematically search for solutions and ensuring that the queen placement follows the rules of chess. Good luck, and enjoy the challenge!