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,...
Solve the task in PYTHON3.

=====
Write me a Python code to fix of b, but a ≠ b;?
assistant
#Here is Python code to fix of b, but a ≠ b;
.

import math
c = int(input())

for _ in range(c):
    length =  int(input())
    arr = [int(item) for item in input().split()]
    new_arr = []

    for index,val in enumerate(arr):
        new_arr.append((val,index))

    def reArrange(arr):
        n = len(arr)
        if n == 0:
            return []
    
        g_list = sorted(arr,reverse=True)
        # meaningless weight -> 'heap'

        top = g_list[0][0]

        stop_index = 0

        result_list = []

        while len(g_list) != 0:
            while stop_index + 1 <= len(g_list) - 1 and g_list[stop_index][0] == g_list[stop_index+1][0]:
                stop_index += 1 

            result_list += sorted([arr[i[1]][0] for i in g_list[:stop_index+1]],reverse=True)

            g_list = g_list[stop_index+1:]

            if len(g_list) == 0:
                break
    
            t_list = []

            for count in range(len(g_list)):
                p = math.gcd(top,g_list[count][0])
                t_list.append((p,g_list[count][1]))

            g_list = sorted(t_list,reverse=True)

            top = g_list[0][0]

            stop_index = 0

        return result_list
        
    print(*reArrange(new_arr))