<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 totalNQueens(int n) {
        unordered_set<int> cols;
        unordered_set<int> posDiag;
        unordered_set<int> negDiag;

        return helper(n, 0, cols, posDiag, negDiag);
    }

private:
    int helper(const int& n, int row, unordered_set<int> cols,
                unordered_set<int> posDiag, unordered_set<int> negDiag) {
        if (row == n) {
            return 1;
        }

        int ret = 0;

        for (int col = 0; col < n; col++) {
            if (cols.find(col) == cols.end() &&
                posDiag.find(row + col) == posDiag.end() &&
                negDiag.find(row - col) == negDiag.end()) {
                cols.insert(col);
                posDiag.insert(row + col);
                negDiag.insert(row - col);
                ret += helper(n, row + 1, cols, posDiag, negDiag);
                cols.erase(col);
                posDiag.erase(row + col);
                negDiag.erase(row - col);
            }
        }

        return ret;
    }
};
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