<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 {
    vector<vector<string>> res;
    void helper(int row, int n, vector<pair<int,int>> &positions, vector<string> &ans){
        if(row==n) {
            res.push_back(ans);
            return;
        }
        string temp(n,'.');
        unordered_set<int> st;
        for(auto x: positions){
            st.insert(x.second);
            if(x.second+row-x.first<n) st.insert(x.second+row-x.first);
            if(x.second+row-x.first>=0) st.insert(x.second+x.first-row);
        }
        for(int i=0; i<n; i++){
            if(st.find(i)!=st.end()) continue;
            temp[i]='Q';
            positions.push_back({row,i});
            ans.push_back(temp);
            helper(row+1, n, positions, ans);
            positions.pop_back();
            ans.pop_back();
            temp[i]='.';
        }
    }
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<pair<int,int>> positions;
        vector<string> ans;
        helper(0, n, positions, ans);
        return res;
    }
};
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