<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>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</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> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
    void backtrack(int n,int row, vector<string> output,vector<bool> upperCol,vector<bool> rightDiag,vector<bool> leftDiag,int &cnt){

        if(row==n){
            cnt++;
            return;
        }
        
        for(int col=0;col<n;col++){
            if(upperCol[col]==0 && rightDiag[row+col]==0 && leftDiag[row-col+n-1]==0){
                output[row][col]='Q';
                upperCol[col]=1;
                rightDiag[row+col]=1;
                leftDiag[row-col+n-1]=1;
                backtrack(n,row+1,output,upperCol,rightDiag,leftDiag,cnt);
                output[row][col]='.';
                upperCol[col]=0;
                rightDiag[row+col]=0;
                leftDiag[row-col+n-1]=0;
            }
        }
    }

    int totalNQueens(int n) {
        vector<string> output(n, string(n, '.'));
        vector<bool> upperCol(n,0),rightDiag(2*n-1,0),leftDiag(2*n-1,0);
        int ans=0;
        backtrack(n,0,output,upperCol,rightDiag,leftDiag,ans);
        return ans;
    }
};
17657