<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 cnt;
   bool isValid(vector<string> &grid, int n,int row,int col) {
      vector<pair<int,int>> vp;
      for(int i=0;i<row;i++) {
        for(int j=0;j<n;j++) {
           if(grid[i][j]=='Q') vp.push_back({i,j});
        }
      }
      if(row==0) return true;
      for(int i=0;i<vp.size();i++) {
          int x = abs(row-vp[i].first);
          int y = abs(col-vp[i].second);
          if(y==0 || x==y) return false;
      }
      return true;
   }



   void solve(vector<string> &grid, int n,int row) {
        if(row==n) {
            cnt++;
          
        }

        for(int i=0;i<n;i++) {
            if(isValid(grid,n,row,i)) {
                grid[row][i]='Q';
                solve(grid,n,row+1);
                grid[row][i]='.';
            }
        }

      return;
   }


    int totalNQueens(int n) {
         
          vector<string> grid;
          for(int i=0;i<n;i++) {
            string s(n,'.');
            grid.push_back(s);
          }
          
          int row=0;
          solve(grid,n,row);
          return cnt;
    }
};
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