<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 mark(vector<vector<bool>> &marker,int i,int j,int n){
        for(int k=0;k<n;k++){
            marker[i][k]=false;
            marker[k][j]=false;
        }
        int tempi=i,tempj=j;
        while(tempi>=0 && tempj>=0){
            marker[tempi][tempj]=false;
            tempi--;
            tempj--;
        }
        tempi=i,tempj=j;
        while(tempi>=0 && tempj<n){
            marker[tempi][tempj]=false;

            tempi--;
            tempj++;
        }
        tempi=i,tempj=j;
        while(tempi<n && tempj<n){
            marker[tempi][tempj]=false;

            tempi++;
            tempj++;
        }
        tempi=i,tempj=j;
        while(tempi<n && tempj>=0){
            marker[tempi][tempj]=false;

            tempi++;
            tempj--;
        }
    }

    void make(string &temp, int j,int n){
        for(int i=0;i<n;i++){
            if(i==j){
                temp+='Q';
            }
            else temp+='.';
        }
    }

    void mprint(vector<vector<bool>> &marker,int n){
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(marker[i][j]) cout<<1;
                else cout<<0;
            }
            cout<<endl;
        }
        cout<<endl;
    }

    void print(vector<string> curr){
        for(int i=0;i<curr.size();i++){
            cout<<curr[i]<<endl;
        }
        cout<<endl;
    }

    void help(int i,int n, vector<vector<bool>> marker, vector<vector<string>> &ans, vector<string> curr, int queen){
        if(queen == n){
            ans.push_back(curr);
            return;
        }
        for(int j=0;j<n;j++){
            if(marker[i][j]){
                vector<vector<bool>> curr_mark=marker;
                mark(curr_mark,i,j,n);
                //mprint(curr_mark,n);
                string temp="";
                make(temp,j,n);
                curr.push_back(temp);
                help(i+1,n,curr_mark,ans,curr,queen+1);
                print(curr);
                curr.pop_back();
            }
        }
    }
    int totalNQueens(int n) {
        vector<vector<bool>> marker(n,vector<bool> (n,true));
        vector<vector<string>> ans;
        vector<string> curr;
        int queen=0;
        help(0,n,marker,ans,curr,queen);
        return ans.size();
    }
};
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