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,...
# -*- Can you provide a Python program to fix of b, but a ≠ b;?
assistant
#Here is Python program to fix of b, but a ≠ b;
.
 coding: utf-8 -*-
# import bisect
# import heapq
# import math
# import random
# from collections import Counter, defaultdict, deque
# from decimal import ROUND_CEILING, ROUND_HALF_UP, Decimal
# from fractions import Fraction
# from functools import lru_cache, reduce
# from itertools import combinations, combinations_with_replacement, product, permutations, accumulate
# from operator import add, mul, sub, itemgetter, attrgetter

import sys
# sys.setrecursionlimit(10**6)
# readline = sys.stdin.buffer.readline
readline = sys.stdin.readline

INF = 2**62-1

def read_int():
    return int(readline())

def read_int_n():
    return list(map(int, readline().split()))

def read_float():
    return float(readline())

def read_float_n():
    return list(map(float, readline().split()))

def read_str():
    return readline().strip()

def read_str_n():
    return readline().strip().split()

def ep(*args):
    print(*args, file=sys.stderr)

def mt(f):
    import time

    def wrap(*args, **kwargs):
        s = time.perf_counter()
        ret = f(*args, **kwargs)
        e = time.perf_counter()

        ep(e - s, 'sec')
        return ret

    return wrap

import math
from itertools import combinations
from collections import Counter

# @mt
def slv(N, A):
    if N == 1:
        return A

    ans = []

    ac = Counter(A)
    g = 0
    for _ in range(N):
        # print(ac)
        mg = (-1, -1)
        for k, v in ac.items():
            if v == 0:
                continue
            mg = max(mg, (math.gcd(g, k), k))
        ans.append(mg[1])
        ac[mg[1]] -= 1
        g = mg[0]

    return ans

def main():
    for _ in range(read_int()):
        N = read_int()
        A = read_int_n()
        print(*slv(N, A))

if __name__ == '__main__':
    main()