<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

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

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

from typing import List

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        def backtrack(row: int):
            if row == n:
                # All queens are placed correctly, add the current board to the results
                board_copy = ["".join(row) for row in board]
                results.append(board_copy)
                return

            for col in range(n):
                if col in columns or (row - col) in main_diagonals or (row + col) in anti_diagonals:
                    continue  # Skip if the column or diagonal is already occupied

                # Place the queen
                board[row][col] = 'Q'
                columns.add(col)
                main_diagonals.add(row - col)
                anti_diagonals.add(row + col)

                # Recurse to the next row
                backtrack(row + 1)

                # Remove the queen (backtrack)
                board[row][col] = '.'
                columns.remove(col)
                main_diagonals.remove(row - col)
                anti_diagonals.remove(row + col)

        # Initialize variables
        results = []
        board = [['.' for _ in range(n)] for _ in range(n)]
        columns = set()
        main_diagonals = set()
        anti_diagonals = set()

        # Start backtracking from the first row
        backtrack(0)

        return results

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