<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(vector<int> tmp, int i)
    {
        if(tmp.size()==0)
        return true;

        int y = tmp.size();
        int x = i;

        for(int j=0;j<tmp.size();j++)
        {
            if(tmp[j]==i)
            return false;
            if((y-x) == (j-tmp[j]))
            return false;
            if(abs(x+y) == abs(j+tmp[j]))
            return false;
        }
        return true;
    }
    void findAll(int index, int n, vector<int> &tmp, int &result)
    {
        if(index == n)
        {
            result++;
            return;
        }
        for(int i=0;i<n;i++)
        {
            if(isValid(tmp, i))
            {
                 tmp.push_back(i);
                 findAll(index+1, n, tmp, result);
                 tmp.pop_back();
            }
        }
       
    }
public:
    int totalNQueens(int n) {
        int result=0;
        vector<int> tmp;
        findAll(0, n, tmp, result);
        return result;
    }
};

//    0 1 2 3 4
// 0     
// 1   
// 2           
// 3    p       
// 4   p
14052