<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 check_uncheck(vector<vector<int>> &vis , int val , int i , int j , int n){
        for(int k = 0 ; k < n ; k++){
            vis[i][k] += val ;
            vis[k][j] += val ;
            if(i-k >= 0 && j-k >= 0 ){
                vis[i-k][j-k] += val ;
            }
            if( i+k < n && j+k < n ){
                vis[i+k][j+k] += val ;
            }
            if(i-k >= 0 && j+k < n ){
                vis[i-k][j+k] += val ;
            }
            if(i+k  < n && j-k >= 0 ){
                vis[i+k][j-k] += val ;
            }
        }

    }
    void helper(vector<vector<int>> vis , vector<vector<string>> &ans , vector<string> &temp , int i , int n){
        for(int j = 0 ; j < n ; j++){
            if(vis[i][j] == 0){
                temp[i][j] = 'Q' ; 
                if(i == n-1){
                    ans.push_back(temp) ;
                    temp[i][j] = '.' ;
                    return ; 
                }
                check_uncheck(vis , 1, i , j , n); 
                helper(vis , ans, temp , i+1 , n) ;
                temp[i][j] = '.' ;
                check_uncheck(vis , -1 , i , j , n);
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<int>> vis(n , vector<int>(n , 0)) ;
        vector<vector<string>> ans ;
        string def(n, '.');
        vector<string> temp(n, def);
        helper(vis , ans , temp , 0 , n) ; 
        return ans ;
    }
};
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