<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>

class Solution {
public:
    int queenCount(int n, set<int> cols, set<int> posDiag, set<int> negDiag, int row)
    {
        if(row == n)
        {
            return 1;
        }
        int count = 0;
        for(int i=0; i<n; i++)
        {
            if(cols.find(i) == cols.end() && posDiag.find(row + i) == posDiag.end() && negDiag.find(row - i) == negDiag.end())
            {
                cols.insert(i);
                posDiag.insert(row + i);
                negDiag.insert(row - i);
                count += queenCount(n, cols, posDiag, negDiag, row+1);
                cols.erase(i);
                posDiag.erase(row + i);
                negDiag.erase(row - i);
            }
        }
        return count;
    }
    int totalNQueens(int n) {
       set<int> cols;
       set<int> posDiag;
       set<int> negDiag;
       return queenCount(n, cols, posDiag, negDiag, 0); 
    }
};
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