<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 totalNQueens(int n) {
        
//     }
// };
class Solution {
    bool safe(int i,int j,int x,int y){
        if(y==j || (abs(i-x)==abs(j-y)) || i==x) return false;
        return true;
    }
    bool isOk(vector<vector<int>>& placed,int i,int j){
        for(auto pos : placed){
            if(!safe(pos[0],pos[1],i,j)) return false;
        }
        return true;
    }
    void help(int n,int row,vector<vector<int>>& placed,int q,int& cnt){
        if(row==n){
            if(!q) cnt++;
            return;
        }
        //
        for(int i=0;i<n;i++){
            if(isOk(placed,row,i)){
                placed.push_back({row,i});
                help(n,row+1,placed,q-1,cnt);
                placed.pop_back();
            }
        }
    }
public:

    int totalNQueens(int n) {
        int row = 0 ,cnt = 0;
        vector<vector<int>> placed;
        help(n,row,placed,n,cnt);
        return cnt;
    }
};
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