<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 changePlacementMatrix(vector<vector<bool>> &placementMatrix, int x, int y,int n){
        for(int i=0;i<n;i++){
            placementMatrix[x][i] = true;
            placementMatrix[i][y] = true; 
            if((x+i<n and x+i>=0) && (y+i<n and y+i>=0)){
                placementMatrix[x+i][y+i]=true;
            }
            if((x+i<n and x+i>=0) && (y-i<n and y-i>=0)){
                placementMatrix[x+i][y-i]=true;
            }
            if((x-i<n and x-i>=0) && (y+i<n and y+i>=0)){
                placementMatrix[x-i][y+i]=true;
            }
            if((x-i<n and x-i>=0) && (y-i<n and y-i>=0)){
                placementMatrix[x-i][y-i]=true;
            }
        }

    }
    void solve(int n, vector<vector<string>> &result, vector<string> &output, int curr_col, vector<vector<bool>> &placementMatrix){
        if(curr_col==n){
            result.push_back(output);
            return;    
        }
        
        for(int i=0;i<n;i++){
            if(placementMatrix[i][curr_col]==false){
                string op(n,'.');
                op[i] = 'Q';
                output.push_back(op);
                vector<vector<bool>> copy(placementMatrix);
                changePlacementMatrix(placementMatrix,i,curr_col,n);
                solve(n,result,output,curr_col+1,placementMatrix);
                output.pop_back();
                placementMatrix = copy;
            }
        }
        return;

    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> result;
        vector<string> output;
        vector<vector<bool>> placementMatrix(n, vector<bool>(n,false));
        solve(n,result,output,0,placementMatrix);
        return result;
    }
};
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