<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) {
        vector<vector<int> > v;
        vector<int> row(n,0);
        for(int i=0;i<n;i++){
            v.push_back(row);
        }
        int count = 0;
        combinations(v,0,count);
        return count;
    }
    void combinations(vector<vector<int> > v,int row,int &count){
        if(row == (v.size() - 1)){
            for(int i=0;i<v.size();i++){
                if(v[row][i] == 0){
                    count++;
                }
            }
        }else if(row < v.size()){
            for(int i=0;i<v.size();i++){
                if(v[row][i] == 0){
                    vector<vector<int> > temp(v);
                    int left = i - 1;
                    int right = i + 1;
                    for(int j=row+1;j<temp[row].size();j++){
                        temp[j][i] = 1;
                        if(left >= 0){
                            temp[j][left] = 1;
                            left--;
                        }
                        if(right < temp.size()){
                            temp[j][right] = 1;
                            right++;
                        }
                    }
                    combinations(temp,row+1,count);
                }
            }
        }
    }
};
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