<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 {
private:
    int solve(int n, vector<vector<bool>> places, int idx) {
        if(idx == n) return 1;
        int ans = 0;
        for(int i = 0; i < n; i++) {
            if(places[idx][i]) {
                vector<vector<bool>> temp = places;
                for(int J = idx; J < n; J++) temp[J][i] = false;
                int I = idx, J = i;
                while(I < n && J < n) temp[I++][J++] = false;
                I = idx, J = i;
                while(I < n && J >= 0) temp[I++][J--] = false;
                ans += solve(n, temp, idx + 1);
            }
        }
        return ans;
    }
public:
    int totalNQueens(int n) {
        vector<vector<bool>> places(n, vector<bool>(n,true));
        return solve(n, places, 0);
    }
};
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