<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 {
public:
    void solve(int col, int n, vector<string>& board,
               vector<vector<string>>& ans, vector<int> leftRow,
               vector<int> leftDiagonal, vector<int> lowerDiagonal) {
        if (col == n) {
            ans.push_back(board);
            return;
        }
        for (int row = 0; row < n; row++) {
            if (leftRow[row] == 0 && leftDiagonal[n - 1 + col - row] == 0 &&
                lowerDiagonal[row + col] == 0) {
                leftRow[row] = 1;
                leftDiagonal[n - 1 + col - row] = 1;
                lowerDiagonal[row + col] = 1;
                board[row][col] = 'Q';

                solve(col + 1, n, board, ans, leftRow, leftDiagonal,
                      lowerDiagonal);

                leftRow[row] = 0;
                leftDiagonal[n - 1 + col - row] = 0;
                lowerDiagonal[row + col] = 0;
                board[row][col] = '.';
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<string> board(n,string (n, '.'));

        vector<int> leftRow(n, 0), leftDiagonal(2 * n - 1, 0),
            lowerDiagonal(2 * n - 1, 0);

        solve(0, n, board, ans, leftRow, leftDiagonal, lowerDiagonal);

        return ans;
    }
};
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