<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 bt(int r, int n, unordered_set<int> off, unordered_set<int> on, unordered_set<int> cols){
        if(r == n) return 1;
        int s = 0;
        for(int c = 0; c < n; c++){
            int o = r + c;
            int oo = r - c;
            if(off.find(oo) == off.end() && on.find(o) == on.end() && cols.find(c) == cols.end() ){
                off.insert(oo);
                on.insert(o);
                cols.insert(c);
                s += bt(r + 1, n, off, on, cols);
                off.erase(oo);
                on.erase(o);
                cols.erase(c);
            }
        }
        return s;
    }
    int totalNQueens(int n) {
        unordered_set<int> off;
        unordered_set<int> on;
        unordered_set<int> cols;
        return bt(0, n, off, on , cols);
    }
};
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