<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 {
public:
    vector<vector<char>> grid;
    vector<vector<string>> result;

    bool canPlaceQueen(int r, int c, int n) {
        // row check
        for (int i=0; i<r;i++) {
            if (grid[i][c]=='Q') return false;
        }
        // left diagonal check
        for (int i = r - 1, j = c - 1; i >= 0 && j >= 0; i--, j--) {
            if (grid[i][j] == 'Q') return false;
        }
        // right diagonal check
        for (int i=r-1, j=c+1;i>=0 && j<n;i--,j++) {
            if (grid[i][j]=='Q') return false;
        }
        return true;
    }

    void f(int row,int n) {
        if (row==n) {
            vector<string> temp;
            for (int i=0; i<n;i++) {
                string res="";
                for (int j=0; j<n;j++) {
                    res += grid[i][j];
                }
                temp.push_back(res);
            }
            result.push_back(temp);
            return;
        }
        for (int col=0;col<n;col++) {
            if (canPlaceQueen(row,col,n)) {
                grid[row][col]='Q';
                f(row+1,n);
                grid[row][col]='.'; // restore the grid
            }
        }
    }

    int totalNQueens(int n) {
        result.clear();
        grid.clear();
        grid.resize(n,vector<char>(n, '.'));
        f(0, n);
        return result.size();
    }
};
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