The N-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other. A queen can attack horizontally, vertically, or diagonally.Given an integer n, return the number of distinct solutions to the n-queens puzzle.ExampleInput:4Output:2Explanation:There are two distinct solutions to the 4-queens puzzle as shown.Input format :The input consists of a single integer N, representing the size(N*N) of the chessboard.Output format :The output displays an integer that gives the distinct solutions to the n-queens puzzle.Refer to the sample output format for the formatting specifications.Code constraints :In the given scenario, the test cases will fall under the following constraints:2 <= N <=10Sample test cases :Input 1 :4Output 1 :2Input 2 :3Output 2 :0Input 3 :9Output 3 :352

The N-queens puzzle is a classic problem in computer science and mathematics. It involves placing N queens on an N x N chessboard in such a way that no two queens threaten each other. This means that no two queens can be in the same row, column, or diagonal.

Here's a step-by-step guide on how to solve the N-queens puzzle:

1. Initialize the chessboard: Create an N x N matrix and initialize all cells with 0, which means no queen is placed in any cell at the start.

2. Place the queens: Start from the first row and place a queen in each cell one by one. After placing a queen, check for clashes with already placed queens. In the current row, if we find a cell in the column where there is no clash, we mark this cell and move to the next row. If we do not find such a cell, we return false.

3. Check for clashes: If a queen is placed in a cell, we need to check for clashes with already placed queens. There are three possibilities where a queen can clash with another queen:

   • In the same row: No two queens can be in the same row.
   • In the same column: No two queens can be in the same column.
   • On the same diagonal: No two queens can be on the same diagonal.

4. Backtracking: If we have placed a queen that results in a clash with another queen, we need to backtrack and remove the queen from the current cell and move to the next cell in the same row.

5. Count the solutions: If we have successfully placed all the queens on the board, we have found a solution. We then backtrack and try to find more solutions by moving the queen in the current row to the next cell and checking if it leads to a solution.

6. Return the count of solutions: After we have tried all possible placements in all rows, we return the count of solutions.

The number of distinct solutions for the N-queens puzzle varies with N. For example, there are 2 distinct solutions for N=4, 0 for N=3, and 352 for N=9.