python3

javascript

java

Count all solutions in N-Queen Problem

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.
Given an integer n, return the number of distinct solutions to the n-queens puzzle.


### Input Format

The first line contains an integer N, denoting the size of the board in NxN format.

### Output Format

Print the number of discrete solutions to the n-queens puzzle.

### Example 1:
```txt
Input:
    1
Output:
    1
Explanation:
    For a 1x1 board, there can only be one queen.
```

### Example 2:
```txt
Input:
    10
Output:
    724
Explanation:
    For a 10x10 board there can be 724 distinct solutions.
```

#### Constraints:
- 1 <= n <= 15
