<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:
    bool isSafe(int n,int row, int col, vector<int>colp, vector<int>ldia, vector<int>rdia){
        if(colp[col] || ldia[n+row-col] || rdia[row+col]) return false;
        else return true;
    }
    int helper(int n, int row,vector<int>&colp, vector<int>&ldia, vector<int>&rdia){
        if(row==n) return 1;
        int ans=0;
        for(int col=0;col<n;col++){
            if(isSafe(n,row,col,colp,ldia,rdia)){
                colp[col]=1;
                ldia[n+row-col]=1;
                rdia[row+col]=1;
                ans+=helper(n,row+1,colp,ldia,rdia);
                colp[col]=0;
                ldia[n+row-col]=0;
                rdia[row+col]=0;
            }
        }
        return ans;
    }
    int totalNQueens(int n) {
        vector<int>colp(n,0);
        vector<int>ldia(2*n,0);
        vector<int>rdia(2*n,0);
        return helper(n,0,colp,ldia,rdia);
    }
};
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