<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:
    int size;
    int queens(vector<vector<int>> board,int idx,vector<bool> vert,vector<bool> hori,vector<bool> right,vector<bool> left)
    {
        if(idx==-1)
            return 1;
        int sum=0;
        for(int i=0;i<size;i++)
        {
            int ivert=i;
            int iright=idx-i+size-1;
            int ileft=idx+i;
            if(!vert[ivert]&&!right[iright]&&!left[ileft])
            {
                vert[ivert]=1;
                right[iright]=1;
                left[ileft]=1;
                sum+=queens(board,idx-1,vert,hori,right,left);
                vert[ivert]=0;
                right[iright]=0;
                left[ileft]=0;
            }
        }
        return sum;
    }

    int totalNQueens(int n) {
        vector<vector<int>> board(n,vector<int>(n,0));
        vector<bool> vert(n,0);
        vector<bool> hori(n,0);
        vector<bool> right(2*n-1,0);
        vector<bool> left(2*n-1,0);
        size=n;
        return queens(board,n-1,vert,hori,right,left);
        
    }
};
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