<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 {
public:
    void f(int i,int n,vector<vector<string>> &v,set<int> &c,set<int> &diff,set<int> &sum,vector<string> &curr) {
        // cout<<i<<endl;
        if(i==n) {
            v.push_back(curr); 
            return ;
        }
        for(int j=0;j<n;j++) {
            if(c.find(j) == c.end() && diff.find((i-j))==diff.end() && sum.find(abs(i+j))==sum.end()) {
                c.insert(j); 
                diff.insert((i-j)); 
                sum.insert(abs(i+j)); 
                string str(n,'.'); 
                str[j]='Q'; 
                curr.push_back(str);
                f(i+1,n,v,c,diff,sum,curr); 
                curr.pop_back(); 
                diff.erase((i-j)); 
                sum.erase(abs(i+j)); 
                c.erase(j); 
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> v; 
        set<int> c,diff,sum; 
        vector<string> curr;
        f(0,n,v,c,diff,sum,curr); 
        return v;
    }
};
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