<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:
    def totalNQueens(self, n: int) -> int:

        cnt = [0]
        diag, ndiag, col = set(), set(), set()

        def backtrack(row):
            if row == n:
                cnt[0] = cnt[0] + 1
                return

            for c in range(n):
                if c in col or (row+c) in diag or (row-c) in ndiag:
                    continue

                col.add(c)
                diag.add(row+c)
                ndiag.add(row-c)

                backtrack(row+1)

                col.remove(c)
                diag.remove(row+c)
                ndiag.remove(row-c)
        
        backtrack(0)
        return cnt[0]

        
16100