#include<stdio.h>
#include<algorithm>
#include<math.h>
using namespace std;
long long b[110000];
long long gz[550];
double eps=1e-9;
int main(){
	int a;
	while(scanf("%d",&a),a){
		long double A=1;
		int sz=0;
		for(int i=0;i<(a+1)*a/2;i++){
			scanf("%lld",b+i);
			if(b[i]%2==0){
				A*=pow(b[i],1.0/a);
				gz[sz++]=b[i];
			}else A*=pow(b[i],-1.0/a/(a-1));
		}
		long long gs=(long long)(A+0.5);
		printf("%lld\n",gs);
		std::sort(gz,gz+a);
		for(int i=0;i<a;i++){
			if(i)printf(" ");
			printf("%lld",gz[i]/gs);
		}
		printf("\n");
	}
}
### Prompt

Your challenge is to write 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<stdio.h>
#include<algorithm>
#include<math.h>
using namespace std;
long long b[110000];
long long gz[550];
double eps=1e-9;
int main(){
	int a;
	while(scanf("%d",&a),a){
		long double A=1;
		int sz=0;
		for(int i=0;i<(a+1)*a/2;i++){
			scanf("%lld",b+i);
			if(b[i]%2==0){
				A*=pow(b[i],1.0/a);
				gz[sz++]=b[i];
			}else A*=pow(b[i],-1.0/a/(a-1));
		}
		long long gs=(long long)(A+0.5);
		printf("%lld\n",gs);
		std::sort(gz,gz+a);
		for(int i=0;i<a;i++){
			if(i)printf(" ");
			printf("%lld",gz[i]/gs);
		}
		printf("\n");
	}
}
```