<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:
    bool check(vector<pair<int, int>> queens, int i, int j) {
        for(int k = 0; k < queens.size(); ++k) {
            if(queens[k].first == i) {
                return false;
            }
            if(abs(queens[k].first - i) == abs(queens[k].second - j)) {
                return false;
            }
        }
        return true;
    }
    void nextqueen(vector<pair<int, int>>& queens, int n, vector<vector<string>>& ans) {
        if(queens.size() == n) {
            vector<string> blank;
            for(int i = 0; i < n; ++i) {
                string a = "";
                for(int j = 0; j < n; ++j) {
                    a.push_back('.');
                }
                blank.push_back(a);
            }
            for(int k = 0; k < queens.size(); ++k) {
                blank[queens[k].first][queens[k].second] = 'Q';
            }
            ans.push_back(blank);
        }
        for(int i = 0; i < n; ++i) {
            int j = queens[queens.size() - 1].second + 1;
            if(check(queens, i, j)) {
                queens.push_back(make_pair(i, j));
                nextqueen(queens, n, ans);
                queens.pop_back();
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        
        vector<pair<int, int>> queens;
        for(int i = 0; i < n; ++i) {
            queens = {make_pair(i, 0)};
            nextqueen(queens, n, ans);
        }
        return ans;
    }
};
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