United We Stand

Description:

Input:

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 100$$$) — the length of array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of array $$$a$$$.

Output:

For each test case, output a single integer $$$-1$$$ if a solution does not exist.

Otherwise, in the first line, output two integers $$$l_b$$$ and $$$l_c$$$ — the lengths of arrays $$$b$$$ and $$$c$$$ respectively.

In the second line, output $$$l_b$$$ integers $$$b_1, b_2, \ldots, b_{l_b}$$$ — the elements of array $$$b$$$.

In the third line, output $$$l_c$$$ integers $$$c_1, c_2, \ldots, c_{l_c}$$$ — the elements of array $$$c$$$.

If there are multiple solutions, output any of them. You can output the elements of the arrays in any order.

Sample Input:

5
3
2 2 2
5
1 2 3 4 5
3
1 3 5
7
1 7 7 2 9 1 4
5
4 8 12 12 4

Sample Output:

-1
3 2
1 3 5 
2 4 
1 2
1 
3 5 
2 5
1 1 
2 4 7 7 9 
3 2
4 8 4 
12 12 

Note:

In the first test case, a solution does not exist.

In the second test case, we can obtain $$$b = [1, 3, 5]$$$ and $$$c = [2, 4]$$$. Then elements $$$2$$$ and $$$4$$$ do not divide elements $$$1, 3$$$ and $$$5$$$.

In the fifth test case, we can obtain $$$b = [4, 8, 4]$$$ and $$$c = [12, 12]$$$.