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,...
from
assistant
#Here is Python code to fix of b, but a ≠ b;
.
sys import stdin, stdout

class SOLVE:
    def GCD(self, a, b):
        if a == 0:
            return b
        return self.GCD(b%a, a)
    
    def solve(self):
        R = stdin.readline
        W = stdout.write

        ans = []
        for i in range(int(input())):
            n = int(R())
            a = [int(x) for x in R().split()]
            
            a.sort(reverse = True)
            ans += [str(a[0]) + ' ']
            
            gcd  = a[0]
            a[0] = -1
            for j in range(n-1):
                mx = pos = 0
                for k in range(n):
                    if a[k] != -1:
                        tmp = self.GCD(gcd, a[k])
                        if tmp > mx:
                            mx  = tmp
                            pos = k
                ans   += [str(a[pos]) + ' ']
                a[pos] = -1
                gcd    = mx
            ans += ['\n']

        W(''.join(ans))
    
def main():
    s = SOLVE()
    s.solve()
main()