<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) {
        int counter=0;
        string s(n,'.');
        vector<string> temp(n,s);
        vector<int> leftRow(n,0), lowerDiagonal(2*n-1,0), upperDiagonal(2*n-1,0);

        stack<tuple<int, int, vector<string>, vector<int>, vector<int>, vector<int>>> st;
        st.push({0,n,temp,leftRow,lowerDiagonal,upperDiagonal});
        while (!st.empty()){
            auto [col,size,temp,left,lower,upper]=st.top();
            st.pop();
            if(col==size) {
                counter++;
                continue;
            }
            for(int i=0;i<size;i++) {
                if(left[i]==0 and lower[i+col]==0 and upper[size-1+col-i]==0){
                    left[i]=1;
                    lower[i+col]=1;
                    upper[size-1+col-i]=1;
                    temp[i][col]='Q';

                    st.push({col+1,size,temp,left,lower,upper});

                    left[i]=0;
                    lower[i+col]=0;
                    upper[size-1+col-i]=0;
                    temp[i][col]='.';
                }
            }
        }
    return counter;
    }
};
28472