<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 {
    bool isValid(const vector<int>& pos, int l) {
        for (int i = 0; i < l; ++i) {
            if (pos[i] == pos[l] ||
                l-i == std::abs(pos[l]-pos[i]))
                return false;
        }
        return true;
    }
public:
    int totalNQueens(int n) {
        int res = 0;
        vector<int> pos(n+1);
        int l = 0;

        pos[0] = -1;
        while(l >= 0) {
            if (l == n) {
                ++res;
                --l;
            } else {
                do {
                    ++pos[l];    
                } while(pos[l] < n && !isValid(pos, l));
                if (pos[l] >= n) {
                    --l;
                } else {
                    ++l;
                    pos[l] = -1;
                } 
            }
        }    
        return res;
    }
};
7357