<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

void traverse(int row, int n, vector<int> col, vector<vector<int>> valid, int &ans)
{
    if(row == n)
    {
        ans++;
    }
    else
    {
        for(int j = 0; j < n; j++)
        {
            if(col[j])
            {
                if(valid[row][j])
                {
                    vector<vector<int>> backvalid = valid;

                    col[j] = 0;

                    int x = row, y = j;
                    while(x < n && y < n)
                    {
                        valid[x][y] = 0;
                        x++;
                        y++;
                    }

                    x = row; y = j;
                    while(x >= 0 && y >= 0)
                    {
                        valid[x][y] = 0;
                        x--;
                        y--;
                    }

                    x = row; y = j;
                    while(x < n && y >= 0)
                    {
                        valid[x][y] = 0;
                        x++;
                        y--;
                    }

                    x = row; y = j;
                    while(x >= 0 && y < n)
                    {
                        valid[x][y] = 0;
                        x--;
                        y++;
                    }

                    traverse(row+1, n, col, valid, ans);

                    valid = backvalid;
                    col[j] = 1;
                }
            }
        }
    }
}
class Solution {
public:
    int totalNQueens(int n) {
        int ans = 0;
        vector<int> col(n, 1);
        vector<vector<int>> valid(n, vector<int> (n, 1));
        traverse(0, n, col, valid, ans);
        return ans;
    }
};
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