#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

typedef long long lli;

lli gcd(lli x, lli y){ return y ? gcd(y, x%y) : x; }

int main(){
  int n;
  while(cin >> n && n){
    vector<lli> vec[2];
    for(int i=0;i<n*(n+1)/2;i++){
      lli in;
      cin >> in;
      if(in%2) vec[1].push_back(in);
      else vec[0].push_back(in);
    }
    for(int i=0;i<2;i++) sort(vec[i].begin(), vec[i].end());
    lli t = gcd(vec[0][0], vec[1][0]);
    lli a = sqrt(vec[0][0] / t * (vec[0][1] / (vec[1][0] / t)));
    cout << a << endl;
    for(int i=0;i<vec[0].size();i++) cout << vec[0][i] / a << (i+1 == vec[0].size() ? "\n" : " ");
  }
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

typedef long long lli;

lli gcd(lli x, lli y){ return y ? gcd(y, x%y) : x; }

int main(){
  int n;
  while(cin >> n && n){
    vector<lli> vec[2];
    for(int i=0;i<n*(n+1)/2;i++){
      lli in;
      cin >> in;
      if(in%2) vec[1].push_back(in);
      else vec[0].push_back(in);
    }
    for(int i=0;i<2;i++) sort(vec[i].begin(), vec[i].end());
    lli t = gcd(vec[0][0], vec[1][0]);
    lli a = sqrt(vec[0][0] / t * (vec[0][1] / (vec[1][0] / t)));
    cout << a << endl;
    for(int i=0;i<vec[0].size();i++) cout << vec[0][i] / a << (i+1 == vec[0].size() ? "\n" : " ");
  }
}
```