<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:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;

        helper(ans, {}, {}, {}, {}, n); 
        
        return ans;        
    }
private:
    void helper(vector<vector<string>>& ans, vector<string> vec, set<int> cols, set<int> pDiag, set<int> nDiag,int n){
        int r = vec.size();

        if(r==n){
            ans.push_back(vec);
            return;
        }

        string row = "";

        for (int i=0; i<n; i++){
            row+='.';
        }

        for (int i = 0; i<n; i++){
            if(cols.find(i)!=cols.end() || pDiag.find(r+i)!=pDiag.end() || nDiag.find(r-i)!=nDiag.end())
                continue;
            row[i]='Q';
            vec.push_back(row);
            cols.insert(i);
            pDiag.insert(r+i);
            nDiag.insert(r-i);
            helper(ans, vec, cols, pDiag, nDiag, n);
            row[i]='.';
            cols.erase(i);
            pDiag.erase(r+i);
            nDiag.erase(r-i);
            vec.pop_back();            
        }

    }
};
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