Alex has invented a new game for fun. There are n integers at a board and he performs the following moves repeatedly:

1. He chooses three numbers a, b and c written at the board and erases them.
2. He chooses two numbers from the triple a, b and c and calculates their greatest common divisor, getting the number d (d maybe gcd(a,b), gcd(a,c) or gcd(b,c)).
3. He writes the number d to the board two times.

It can be seen that after performing the move n−2 times, there will be only two numbers with the same value left on the board. Alex wants to know which numbers can left on the board possibly. Can you help him?

There are multiple test cases. The first line of input contains an integer T (1≤T≤100), indicating the number of test cases. For each test case:

The first line contains an integer n (3≤n≤500) -- the number of integers written on the board. The next line contains n integers: a1,a2,...,an (1≤ai≤1000) -- the numbers on the board.

For each test case, output the numbers which can left on the board in increasing order.

3

4

1 2 3 4

4

2 2 2 2

5

5 6 2 3 4

1 2

2

1 2 3

 #include <algorithm>

 #include <cstdio>

 #include <cmath>

 #include <cstring>

 #include <iostream>

 #include <cstdlib>

 #include <set>

 #include <vector>

 #include <cctype>

 #include <iomanip>

 #include <sstream>

 #include <climits>

 #include <queue>

 #include <stack>

 using namespace std;

 typedef long long ll;

 #define INF 0X3f3f3f3f

 const ll MAXN = 1e3 + ;

 const ll MOD = 1e9 + ;

 int GCD(int a, int b)

 {

     return b ==  ? a : GCD(b, a % b);

 }

 int num[MAXN];

 int ans[MAXN];

 int main()

 {

     ios::sync_with_stdio();

     int t;

     cin >> t;

     while (t--)

     {

         memset(ans, , sizeof(ans));

         int n;

         cin >> n;

         for (int i = ; i < n; i++)

             cin >> num[i];

         for (int i = ; i < n - ; i++)

             for (int j = i + ; j < n; j++)

                 ans[GCD(num[i], num[j])] = ;

         int cnt = n;

         bool run = true;

         while (cnt-- >=  && run)

         {

             run = false;

             for (int i = ; i <= ; i++)

                 if (ans[i])

                     for (int j = ; j < n; j++)

                     {

                         if (!ans[GCD(num[j], i)])

                         {

                             ans[GCD(num[j], i)] = ;

                             run = true;

                         }

                     }

         }

         bool flag = false;

         for (int i = ; i <= ; i++)

         {

             if (ans[i])

             {

                 if (!flag)

                 {

                     flag = true;

                     cout << i;

                 }

                 else

                     cout << ' ' << i;

             }

         }

         cout << endl;

     }

     return ;

 }