human
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, ..., a_n. Using each of them exactly at once, you're to make such sequence b_1, b_2, ..., b_n that sequence c_1, c_2, ..., c_n is lexicographically maximal, where c_i=GCD(b_1,...,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 ≠ 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 ≤ t ≤ 10^3). Description of the test cases follows.

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

The second line of each test case contains n integers a_1,...,a_n (1 ≤ a_i ≤ 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.

Example

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

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,...
The above is tricky. Write me a correct solution in PYTHON3.
 ... Can you provide a Python code to fix of b, but a ≠ b;?
assistant
#Here is Python code to fix of b, but a ≠ b;
.

import sys
import math
# import numpy as np
fast_reader=sys.stdin.readline
fast_writer=sys.stdout.write
 
def input():
    return fast_reader().strip()
 
# def print(*argv):
#     fast_writer(' '.join((str(i)) for i in argv))
#     fast_writer('\n') 
#############################################################################################
for T in range(int(input())):
    n=int(input())
    a = list(map(int,input().split()))
    m = max(a);count=1
    ans = [m]
    used = [False for i in range(n)]
    for i in range(n):
        if(a[i]==m):
            used[i]=True
            break
    for k in range(1,n):
        mx=1;ind = 0
        for i in range(n):
            if(used[i]==False and math.gcd(a[i],m)>=mx):
                mx = math.gcd(a[i],m)
                el=a[i]
                count = 1
                ind = i
        ans.append(el)
        used[ind]=True
        m = mx
    # print(ans)
    for i in range(n):
        print(ans[i],end = " ")
    print()