<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 check(int level,int col,int total,vector<int> v){
        int temp=col;
        for(int i=level-1;i>=0;i--){
            if(col==0) break;
            if(v[i]==col-1){
                return false;
            }
            col--;
        }
        col=temp;
        for(int i=level-1;i>=0;i--){
            if(col==total) break;
            if(v[i]==col+1){
                return false;
            }
            col++;
        }
        col=temp;
        for(int i=level-1;i>=0;i--){
            if(v[i]==col){
                return false;
            }
        }  
        return true;
    }
    int rec(int level,int total,vector<int> v){
        if(level==total+1){
            return 1;
        }
        int ans=0;
        for(int i=0;i<=total;i++){
             if(check(level,i,total,v)){
                v[level]=i;
                int rec_call=rec(level+1,total,v);
                ans+=rec_call;
             }
        }
        return ans;
    }
    int totalNQueens(int n) {
        vector<int> v(n,-1);
        return rec(0,n-1,v);
    }
};
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