#include<bits/stdc++.h>
using namespace std;
using Int = long long;
using Int2 = __int128_t;
signed main(){  
  cin.tie(0);
  ios::sync_with_stdio(0);
  Int n;
  while(cin>>n,n){
    vector<Int> b(n*(n+1)/2),e,o;
    for(Int i=0;i<(Int)b.size();i++) cin>>b[i];
    for(Int i=0;i<(Int)b.size();i++)
      if(b[i]%2==0) e.push_back(b[i]);
      else o.push_back(b[i]);
    sort(e.begin(),e.end());
    sort(o.begin(),o.end());
    Int a=sqrt((Int)((Int2)e[0]*e[1]/o[0]));
    cout<<a<<endl;
    for(Int i=0;i<n;i++){
      if(i) cout<<" ";
      cout<<e[i]/a;
    }
    cout<<endl;
  }
  return 0;
}
### Prompt

Generate a CPP solution to the following problem:

Problem H: Squid Multiplication

Squid Eiko loves mathematics. Especially she loves to think about integer. One day, Eiko found a math problem from a website.

"A sequence b ={ai + aj | i < j } is generated from a sequence a ={a0 , ... , an | ai is even if i is 0, otherwise ai is odd}. Given the sequence b , find the sequence a ."

This problem is easy for Eiko and she feels boring. So, she made a new problem by modifying this problem .

"A sequence b ={ai *aj | i < j } is generated from a sequence a ={ a0, ... , an | ai is even if  i  is 0, otherwise ai is odd}. Given the sequence b , find the sequence a ."

Your task is to solve the problem made by Eiko.



Input

Input consists of multiple datasets.
Each dataset is given by following formats.


n
b0 b1 ... bn*(n+1)/2-1


n is the number of odd integers in the sequence a. The range of n is 2 ≤ n ≤ 250. bi is separated by a space. Each bi is 1 ≤ bi ≤ 263-1. The end of the input consists of a single 0.

Output

For each dataset, you should output two lines. First line contains a0, an even number in the sequence a. The second line contains n odd elements separated by a space. The odd elements are sorted by increasing order. You can assume that the result is greater than or equal to 1 and less than or equal to 231-1.

Example

Input

3
6 10 14 15 21 35
2
30 42 35
0


Output

2
3 5 7
6
5 7

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
using Int2 = __int128_t;
signed main(){  
  cin.tie(0);
  ios::sync_with_stdio(0);
  Int n;
  while(cin>>n,n){
    vector<Int> b(n*(n+1)/2),e,o;
    for(Int i=0;i<(Int)b.size();i++) cin>>b[i];
    for(Int i=0;i<(Int)b.size();i++)
      if(b[i]%2==0) e.push_back(b[i]);
      else o.push_back(b[i]);
    sort(e.begin(),e.end());
    sort(o.begin(),o.end());
    Int a=sqrt((Int)((Int2)e[0]*e[1]/o[0]));
    cout<<a<<endl;
    for(Int i=0;i<n;i++){
      if(i) cout<<" ";
      cout<<e[i]/a;
    }
    cout<<endl;
  }
  return 0;
}
```