<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        cols=set()
        posDiag=set() #(r+c)
        negDiag=set() #(r-c)
        res=[]
        matrix=[["."]*n for i in range(n)]
        def helper(r):
            if r==n:
                res.append(["".join(row) for row in matrix])
                return 
            for c in range(n):
                if c not in cols and r+c not in posDiag and r-c not in negDiag:
                    cols.add(c)
                    posDiag.add(r+c)
                    negDiag.add(r-c)
                    matrix[r][c]="Q"
                    helper(r+1)
                    cols.remove(c)
                    posDiag.remove(r+c)
                    negDiag.remove(r-c)
                    matrix[r][c]="."
        helper(0)
        return res
            



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