Solve N-Queens Problem

Statement

Given a chessboard of size $N \times N$, determine how many ways $N$ queens can be placed on the board, such that no two queens attack each other.

A queen can move horizontally, vertically, and diagonally on a chessboard. One queen can be attacked by another queen if it is present in the same row, column, or diagonal of that queen.

Example 1

Below is a valid placement of $4$ queens on a $4 \times 4$ chessboard. The $X$ on the board represents a square where a queen is placed: