A16115. United We Stand

Given an array $a$ of length $n$ , containing integers. And there are two initially empty arrays $b$ and $c$ . You need to add each element of array $a$ to exactly one of the arrays $b$ or $c$ , in order to satisfy the following conditions:

- Both arrays $b$ and $c$ are non-empty. More formally, let $l_b$ be the length of array $b$ , and $l_c$ be the length of array $c$ . Then $l_b, l_c \ge 1$ .
- For any two indices $i$ and $j$ ( $1 \le i \le l_b, 1 \le j \le l_c$ ), $c_j$ is not a divisor of $b_i$ .

Output the arrays $b$ and $c$ that can be obtained, or output $-1$ if they do not exist.

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 $a$ .

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.

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 $c = [12, 12]$ .