<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 {
    unordered_set<int> top;
    unordered_set<int> topRight;
    unordered_set<int> topLeft;
    void makeBoard(int row, vector<string> &board, int n, vector<vector<string>> &result) {
        if(row == n) {
            result.push_back(board);
            return;
        }

        for(int col=0; col<n; col++) {
            if(!top.count(col) && !topRight.count(row + col) && !topLeft.count(row - col)) {
                board[row][col] = 'Q';
                top.insert(col);
                topRight.insert(row + col);
                topLeft.insert(row - col);
                
                makeBoard(row + 1, board, n, result);
                
                board[row][col] = '.';
                top.erase(col);
                topRight.erase(row + col);
                topLeft.erase(row - col);
            }
        }

    }
public:
    int totalNQueens(int n) {
        vector<string> board(n, string(n, '.'));        

        vector<vector<string>> result;
        makeBoard(0, board, n, result);

        return result.size();
    }
};
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