<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>

void Aum(vector<vector<string>> &ans, vector<string> &cur, int iter, int n, set<int> col, set<int> sum, set<int> diff){
    if(iter == n){
        vector<string> tempo(cur);
        ans.push_back(tempo);
        return;
    }
    string S;
    for(int aa = 0; aa < n; aa++){S.push_back('.');}
    for(int aa = 0; aa < n; aa++){
        if(col.find(aa) == col.end() && sum.find(aa+iter) == sum.end() && diff.find(aa-iter) == diff.end()){
            col.insert(aa);
            sum.insert(aa+iter);
            diff.insert(aa-iter);
            S[aa] = 'Q';
            cur.push_back(S);
            Aum(ans, cur, iter+1, n, col, sum, diff);
            col.erase(aa);
            sum.erase(aa+iter);
            diff.erase(aa-iter);
            cur.pop_back();
            S[aa] = '.';
        }
    }
}
class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        string S;
        for(int aa = 0; aa < n; aa++){S.push_back('.');}
        vector<vector<string>> um;
        vector<string> A;
        set<int> c;
        set<int> s;
        set<int> d;
        Aum(um, A, 0, n, c, s, d);
        return um;
    }
};
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