Big Vova

1000ms

262144K

Description:

Alexander is a well-known programmer. Today he decided to finally go out and play football, but with the first hit he left a dent on the new Rolls-Royce of the wealthy businessman Big Vova. Vladimir has recently opened a store on the popular online marketplace "Zmey-Gorynych", and offers Alex a job: if he shows his programming skills by solving a task, he'll work as a cybersecurity specialist. Otherwise, he'll be delivering some doubtful products for the next two years.

You're given $$$n$$$ positive integers $$$a_1, a_2, \dots, a_n$$$. Using each of them exactly at once, you're to make such sequence $$$b_1, b_2, \dots, b_n$$$ that sequence $$$c_1, c_2, \dots, c_n$$$ is lexicographically maximal, where $$$c_i=GCD(b_1,\dots,b_i)$$$ - the greatest common divisor of the first $$$i$$$ elements of $$$b$$$.

Alexander is really afraid of the conditions of this simple task, so he asks you to solve it.

A sequence $$$a$$$ is lexicographically smaller than a sequence $$$b$$$ if and only if one of the following holds:

$$$a$$$ is a prefix of $$$b$$$, but $$$a \ne b$$$;
in the first position where $$$a$$$ and $$$b$$$ differ, the sequence $$$a$$$ has a smaller element than the corresponding element in $$$b$$$.

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^3$$$) — the length of the sequence $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,\dots,a_n$$$ ($$$1 \le a_i \le 10^3$$$) — the sequence $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^3$$$.

Output:

For each test case output the answer in a single line — the desired sequence $$$b$$$. If there are multiple answers, print any.

Sample Input:

7
2
2 5
4
1 8 2 3
3
3 8 9
5
64 25 75 100 50
1
42
6
96 128 88 80 52 7
5
2 4 8 16 17

Sample Output:

5 2 
8 2 1 3 
9 3 8 
100 50 25 75 64 
42 
128 96 80 88 52 7 
17 2 4 8 16

Note:

In the first test case of the example, there are only two possible permutations $$$b$$$ — $$$[2, 5]$$$ and $$$[5, 2]$$$: for the first one $$$c=[2, 1]$$$, for the second one $$$c=[5, 1]$$$.

In the third test case of the example, number $$$9$$$ should be the first in $$$b$$$, and $$$GCD(9, 3)=3$$$, $$$GCD(9, 8)=1$$$, so the second number of $$$b$$$ should be $$$3$$$.

In the seventh test case of the example, first four numbers pairwise have a common divisor (a power of two), but none of them can be the first in the optimal permutation $$$b$$$.

Informação

Provedor Codeforces

Código CF1407B