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 ={a_i + a_j | i < j } is generated from a sequence a ={a₀ , ... , a_n | a_i is even if i is 0, otherwise a_i 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 ={a_i *a_j | i < j } is generated from a sequence a ={ a₀, ... , a_n | a_i is even if i is 0, otherwise a_i 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. b_i is separated by a space. Each b_i is 1 ≤ b_i ≤ 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.

Sample input

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

Sample output

2
3 5 7
6
5 7