<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) {
        int res = 0;
        unordered_set<int> col, sum,  substract;
        totalNQueens(res, n, 0, col, sum, substract);
        return res;
    }

private:
    void totalNQueens(int& res, int n, int row, unordered_set<int> col, unordered_set<int> sum, unordered_set<int> substract) {
        if(row == n) {
            ++res;
            return;
        }
        for(int i = 0; i < n; ++i) {
            if(col.count(i) == 1 || sum.count(i + row) == 1 || substract.count(i - row) == 1) {
                continue;
            }
            col.insert(i);
            sum.insert(i + row);
            substract.insert(i - row);
            totalNQueens(res, n, row + 1, col, sum, substract);
            col.erase(i);
            sum.erase(i + row);
            substract.erase(i - row);
        }
    }
};
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