<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:
 vector<vector<string>>ans;
 bool validate(int r,int c, vector<string>mp)
 {
    int a=r;
    int b=c;
    int n=mp.size();
    for(int i=0;i<n;i++)
    {
        if(mp[i][b]=='Q')
        {
            return false;
        }
        if(mp[a][i]=='Q')
        {
            return false;
        }

    }
    while(a>=0&&b>=0)
    {
        if(mp[a][b]=='Q')
        {
            return false;
        }
        a--;
        b--;
    }
    a=r;
    b=c;
    while(a<n&&b>=0)
    {
        if(mp[a][b]=='Q')
        {
            return false;
        }
        a++;
        b--;
    }
    return true;
 }
    int   helper(int c,vector<string>&mp)
     {
        int n=mp.size();
        int ans=0;
        if(c==n)
        {
            
            return 1;
        }
        for(int j=0;j<n;j++)
        {
            if(validate(j,c,mp))
            {
               
                mp[j][c]='Q';
               ans+=  helper(c+1,mp);
                mp[j][c]='.';
                
            }
        }
        return ans;

     }
   int totalNQueens(int n) {
    vector<string>mp;
    for(int i=0;i<n;i++)
    {
        string s="";
        for(int j=0;j<n;j++)
        {
            s+='.';
        }
        mp.push_back(s);
    }
   return  helper(0,mp);
   
    }
};
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