human
Give me a Python code to fix of b, but a ≠ b; given the following:
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.
assistant
#Here is Python code to fix of b, but a ≠ b;
.

# def element(a, s):
#     z = 0
#     x = 0
#     for i in range(len(s)):
#         d = math.gcd(a,s[i])
#         if d>z:
#             z = d
#             x = s[i]
#     return x



# import math
# t = int(input())
# for h in range(t):
#     n1 = int(input())
#     n = list(map(int, input().split()))
#     s = n[:]
#     new = []
#     new.append(max(n))
#     s.remove(new[0])
#     for i in range(n1-1):
#         x = element(new[-1], s)
#         new.append(x)
#         s.remove(x)
#     print(*new)
    

def element(a, s):
    z = 0
    x = 0
    for i in range(len(s)):
        d = math.gcd(a,s[i])
        if d>z:
            z = d
            x = s[i]
    return x , z


import math
t = int(input())
for h in range(t):
    n1 = int(input())
    n = list(map(int, input().split()))
    s = n[:]
    new = []
    new.append(max(n))
    s.remove(new[0])
    if n1 >= 2:
        x,z = element(new[-1], s)
        new.append(x)
        s.remove(x)
    for i in range(n1-2):
        x, z = element(z, s)
        new.append(x)
        s.remove(x)
    print(*new)