p00654 Squid Multiplication_17034
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
import math

while(1):
    n=int(raw_input())
    if n==0:    break
    A=map(int,raw_input().split())
    E=[]
    D=[]
    for a in A:
        if a%2==0:
            E.append(a)
        else:
            D.append(a)
    E.sort()
    D.sort()
    
    g=2
    el=E[0]
    for i in range(100):
        if el>>i%2:
            g**=i
            break
    E=[e/g for e in E]
    
    k1=int(math.sqrt(D[0]*E[0]/E[1]))
    ga =E[0]/k1
    E=[e/ga for e in E]
    
    print int(g*ga)
    print ' '.join(map(str,map(int,E)))