<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 {
private:
    // set to record each queen location fwd_diag(r+c), bwk_diag(r-c)
    std::set<int> col{}, fwd_diag{}, bwk_diag{};

    int count = 0;

    void findPositions(int row, int n)
    {
        if(row == n) {
            count++;
        }
        else {
            for(int column = 0; column < n; column++) {
                if( !col.contains(column) &&
                    !fwd_diag.contains(row + column) &&
                    !bwk_diag.contains(row - column)) {
                        col.insert(column);
                        fwd_diag.insert(row + column);
                        bwk_diag.insert(row - column);


                        findPositions(row + 1, n);

                        col.erase(column);
                        fwd_diag.erase(row + column);
                        bwk_diag.erase(row - column);

                    }
            }

        }
    }

public:
    int totalNQueens(int n) {

        if(n == 1) {
            return 1;
        }
        
        findPositions(0, n);
        return count;
    }
};
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