<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 n, res = 0;
	// Check whether placing a new queen at given point is safe or not
    bool isSafe(vector<string> arr, int x, int y){
        for (int row=0; row<x; row++){
            if (arr[row][y]=='Q'){
                return false;
            }
        }
    
        int row = x;
        int col = y;
        while(row>=0 && col>=0){
            if (arr[row][col]=='Q'){
                return false;
            }
            row--;
            col--;
        }
    
        row = x;
        col = y;
        while(row>=0 && col<n){
            if (arr[row][col]=='Q'){
                return false;
            }
            row--;
            col++;
        }
    
        return true;
    }

    void nQueen(vector<string> &ans, int i){
        if (i>=n){
			// count all the possible answers
            res++;
            return;
        }
        
        for(int k=0;k<n;k++){
            if(isSafe(ans,i,k)){
                ans[i][k] = 'Q';
                nQueen(ans,i+1);
                ans[i][k] = '.';  // backtracking
            }
        }        
    }
    
    int totalNQueens(int num) {
        n = num;
		// initializing vector with ".......n"
        vector<string> ans(n);
        string temp = "";
        for(int j=0;j<n;j++)
            temp+='.';
        
        for(int i=0;i<n;i++)
            ans[i] = temp;
        
        
        nQueen(ans,0);
        return res;
    }
};
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