<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:
    void backtracking (int l,int n,vector<string> at,vector<vector<bool>> hash,set<vector<string>>&out) {
        for (int j=0;j<n;j++) {
            if(hash[l][j]==false) {
                vector<vector<bool>> check=hash;
                vector<string> nat=at;
                nat[l][j]='Q';
                for (int k=0;k<n;k++) {
                    check[l][k]=true;
                    check[k][j]=true;
                }
                int a,b;
                a=l,b=j;
                while(a<n&&b<n&&a>=0&&b>=0) {
                    check[a][b]=true;
                    a++;
                    b++;
                }
                a=l,b=j;
                while(a<n&&b<n&&a>=0&&b>=0) {
                    check[a][b]=true;
                    a--;
                    b--;
                }
                a=l,b=j;
                while(a<n&&b<n&&a>=0&&b>=0) {
                    check[a][b]=true;
                    a--;
                    b++;
                }
                a=l,b=j;
                while(a<n&&b<n&&a>=0&&b>=0) {
                    check[a][b]=true;
                    a++;
                    b--;
                }
                if(l==(n-1)) {
                    out.insert(nat);
                }
                else {
                    backtracking(l+1,n,nat,check,out);
                }
            }
        }
    }
    int totalNQueens(int n) {
        set<vector<string>> out;
        string got="";
        for (int i=0;i<n;i++) {
            got+='.';
        }
        vector<vector<bool>> hash(n,vector<bool> (n,false));
        vector<string> at(n,got);
        backtracking(0,n,at,hash,out);
        vector<vector<string>> sto;
        return out.size();
    }
};
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