<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>> ans;

    void helper(int i,int n,vector<string> curr,vector<vector<int>> valid){
        if(i == n){
            ans.push_back(curr);
            return;
        }

        for(int j = 0;j<n;j++){
            if(valid[i][j] == 0){
                curr[i][j] = 'Q';
                for(int k = i;k<n;k++){
                    valid[k][j]++;
                    if(j+k-i < n) valid[k][j+k-i]++;
                    if(j-k+i >= 0) valid[k][j-k+i]++;
                }
                helper(i+1,n,curr,valid);
                curr[i][j]='.';
                for(int k = i;k<n;k++){
                    valid[k][j]--;
                    if(j+k-i < n) valid[k][j+k-i]--;
                    if(j-k+i >= 0) valid[k][j-k+i]--;
                }
            }
        }

        return;
    }
    vector<vector<string>> solveNQueens(int n) {
        string temp = "";
        for(int i = 0;i<n;i++){
            temp+='.';
        }
        vector<string> curr(n,temp);
        vector<vector<int>> valid(n,vector<int>(n,0));
        helper(0,n,curr,valid);
        return ans;
    }
};
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