<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 helper(int col ,int n, int &res , vector<bool> topDiagonal , 
                    vector<bool> bottomDiagonal , vector<bool> mid) {
        if(col == n) {
            // res.push_back(board);
            res++;
            return;
        }

        for(int row = 0 ; row < n ; row++) {
            if(mid[row] == 0 and topDiagonal[row+col] == 0 and bottomDiagonal[n-1+row-col]==0){
                // board[row][col] = 'Q';
                mid[row]=1;
                topDiagonal[row+col]=1;
                bottomDiagonal[n-1+row-col]=1;
                helper(col+1 , n, res ,topDiagonal,bottomDiagonal,mid);
                // board[row][col] = '.';
                mid[row]=0;
                topDiagonal[row+col]=0;
                bottomDiagonal[n-1+row-col]=0;
            }
        }
    }
    int totalNQueens(int n) {
        // vector<vector<string>> res;
        int res = 0;
        // string s(n,'.');
        // vector<string> board(n,s);
        vector<bool> topDiagonal(2*n-1,0);
        vector<bool> bottomDiagonal(2*n-1,0);
        vector<bool> mid(n,0);
        helper(0,n,res,topDiagonal,bottomDiagonal,mid);
        return res;
    }
};
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