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

# def computeGCD(x, y=1):
#     while (y):
#         x, y = y, x % y
#
#     return x

import math

t = int(input())
while(t):
    t-=1
    n = int(input())
    a = [int(_) for _ in input().split(" ")]
    ans = []
    a.sort()
    b = a[::-1]
    maxx_gcd = b[0]
    # b.pop(0)
    removed_indices = {}
    removed_indices[0] = True
    # curr = math.gcd(60, 48)
    while(len(removed_indices)<len(a)):
        maxx_index = 0
        curr_gcd = maxx_gcd
        maxx_gcd = 1
        for k,v in enumerate(b):
            if k not in removed_indices:
                if math.gcd(v,curr_gcd)>=maxx_gcd:
                    maxx_gcd = math.gcd(v,curr_gcd)
                    maxx_index = k
        removed_indices[maxx_index] = True
        # print(maxx_index, maxx_gcd)
        # curr_gcd = maxx_gcd
    ans = []
    for x in removed_indices:
        ans.append(b[x])
    # print(*removed_indices)
    print(*ans)
    # print(b)

    # print(*ans)