Big Vova

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 $a_1,a_2,\dots ,a_n$. Using each of them exactly at once, you’re to make such sequence $b_1,b_2,\dots ,b_n$ that sequence $c_1,c_2,\dots ,c_n$ is lexicographically maximal, where $c_i=GCD(b_1,\dots ,b_i)$ - 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 $a\ne b$;
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 $t(1\le t\le 10^3)$. Description of the test cases follows.

The first line of each test case contains $a$ single integer $n(1\le n\le 10^3)$ — the length of the sequence $a$.

The second line of each test case contains $n$ integers $a_1,\dots ,a_n(1\le a_i\le 10^3)$ — the sequence $a$.

It is guaranteed that the sum of n over all test cases does not exceed $10^3$.

Output

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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 $c=[5,1]$.

In the third test case of the example, number $9$ should be the first in b, and $GCD(9,3)=3$, $GCD(9,8)=1$, so the second number of b should be $3$.

In the seventh test case of the example, first four numbers pairwise have a common divisor ($a$ power of two), but none of them can be the first in the optimal permutation $b$.

#include <bits/stdc++.h>
using namespace std;
const int maxn=2e5+10;
int a[maxn],n,vis[maxn];
int main() {
    
    
    int _;
    scanf("%d", &_);
    while (_--) {
    
    
        scanf("%d", &n);
        int pre = 1;
        for (int i = 1; i <= n; i++) {
    
    
            vis[i] = 0;
        }
        for (int i = 1; i <= n; i++) {
    
    
            scanf("%d", &a[i]);
            pre = max(pre, a[i]);
        }
        for (int i = 1; i <= n; i++) {
    
    
            int mx = 1, p = -1;
            for (int j = 1; j <= n; j++) {
    
    
                if (vis[j] == 0 && __gcd(a[j], pre) >= mx) {
    
    
                    mx = __gcd(a[j], pre);
                    p = j;
                }
            }
            pre = mx;
            printf("%d ", a[p]);
            vis[p] = 1;
        }
        printf("\n");
    }
    return 0;
}