<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>

class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        ans = []
        board = ['.'*n for _ in range(n)]

        def backtrack(board,row):
            if row == n:
                ans.append(board.copy())
                return
            col = len(board)
            for c in range(col):
                
                #check valid 
                res = self.isvalid(row,c,board)

                if res:

                    board[row] = board[row][:c]+"Q"+board[row][c+1:]

                    backtrack(board,row+1)

                    board[row] = board[row][:c]+"."+board[row][c+1:]
        backtrack(board,0)
        return ans

    def isvalid(self,r,c,board):
        #check top
        for i in range(r):
            if board[i][c] == "Q":
                return False
        #check left top
        for i,j in zip(range(r-1,-1,-1),range(c-1,-1,-1)):
            if board[i][j] == "Q":
                return False
        #check right top
        for i,j in zip(range(r-1,-1,-1),range(c+1,len(board[0]),1)):
            if board[i][j] == "Q":
                return False

        return True


        


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