BestCoder Round #87 1001

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

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

It can be seen that after performing the move n−2n-2n−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 TTT (1≤T≤100)(1 \le T \le 100)(1≤T≤100), indicating the number of test cases. For each test case:

The first line contains an integer nnn (3≤n≤500)(3 \le n \le 500)(3≤n≤500) -- the number of integers written on the board. The next line contains nnn integers: a1,a2,...,ana_1, a_2, ..., a_na​1​​,a​2​​,...,a​n​​ (1≤ai≤1000)(1 \le a_i \le 1000)(1≤a​i​​≤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