<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>

import copy

class Solution:
    def trblNo(self, i, j):
        return i+j
    
    def tlbrNo(self, i, j):
        return i - j
    
    def go(self, nq, row):        
        for col in range(self.n):
            if col not in nq['col']:
                trbl = row+col
                if trbl not in nq['trbl']:
                    tlbr = row-col
                    if tlbr not in nq['tlbr']:                        
                        nnq = copy.deepcopy(nq)
                        nnq['row'].append(row)
                        nnq['col'].append(col)
                        nnq['trbl'].append(trbl)
                        nnq['tlbr'].append(tlbr)
                        if row == self.n-1:
                            self.nqs.append(nnq)
                        else:
                            self.go(nnq, row+1)
            
            

    def totalNQueens(self, n: int) -> int:
        if n == 1:
            return 1
        self.n = n
        self.nqs = []
        for j in range(self.n):
            self.go({'row':[0], 'col':[j], 'trbl':[j], 'tlbr':[-j]}, 1)
        # print(self.nqs)    
        return len(self.nqs)


16800