<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:
    def totalNQueens(self, n: int) -> int:
        
        def solve(r):
            if(r == n):
                result.append(["".join(row) for row in board])
                return
            for c in range(n):
                di = r+c
                rdi = (r-c) + (n-1)
                if(cols[c] == 0 and diag[di]==0 and rdiag[rdi] == 0):
                    cols[c] = diag[di] = rdiag[rdi] = 1
                    board[r][c] = "Q"
                    
                    solve(r+1)
                    
                    cols[c] = diag[di] = rdiag[rdi] = 0
                    board[r][c] = "."
        
        board = [["."]*n for _ in range(n)]
        cols = [0]*n
        diag = [0]*(2*n-1)
        rdiag = [0]*(2*n-1)
        result = []
        solve(0)
        return len(result)
        
        
17000