<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 isPossible(vector<string>&board,int col,int row,vector<int>leftrow,vector<int>upperd,vector<int>lowerd,int n){
        if(leftrow[row] == 1) return false;
        if(lowerd[row+col]==1) return false;
        if(upperd[n-1+col-row]==1) return false;
        return true;
    }
    void solve(int col,vector<vector<string>>&ans,vector<string>&board,vector<int>leftrow,vector<int>upperd,vector<int>lowerd,int n){
        if(col == n){
            ans.push_back(board);
            return;
        }
        for(int i=0;i<n;i++){
            if(isPossible(board,col,i,leftrow,upperd,lowerd,n)){
                board[i][col]='Q';
                leftrow[i] = 1;
                upperd[n-1+col-i] = 1;
                lowerd[i+col] = 1;
                solve(col+1,ans,board,leftrow,upperd,lowerd,n);
                board[i][col]='.';
                leftrow[i] = 0;
                upperd[n-1+col-i] = 0;
                lowerd[i+col] = 0;
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>>ans;
        vector<string>board(n);
        string s(n,'.');
        for(int i=0;i<n;i++){
            board[i]=s;
        }
        vector<int>leftrow(n,0);
        vector<int>upperd(2*n-1,0);
        vector<int>lowerd(2*n-1,0);
        solve(0,ans,board,leftrow,upperd,lowerd,n);
        return ans;
    }
};
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