<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:
    int totalNQueens(int n) {
        vector<bool> col(n,false);
        vector<bool> diag1(2*n, false);
        vector<bool> diag2(2 * n, false);

        function<int(int)> dfsQueens = [&](int row_no){
            if (row_no >= n){
                return 0;
            }
            string s = "";
            for (int i =0; i < n; i ++){
                s += ".";
            }
            int solution = 0;
            for (int i =0; i < n ; i ++){
                if (col[i] || diag1[n + (row_no - i)] || diag2[i + row_no]){
                    continue;
                }
                s[i] = 'Q';
                if (row_no == n - 1){
                    return 1;
                }
                col[i] = true;
                diag1[n + (row_no - i)] = true;
                diag2[i + row_no] = true;
                int results = dfsQueens(row_no + 1);
                solution += results;
                s[i] = '.';
                col[i] = false;
                diag1[n + (row_no - i)] = false;
                diag2[i + row_no] = false;
            }
            return solution;
        };
        return dfsQueens(0);
    }
};
9417