A. United We Standtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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.InputEach 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.OutputFor 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.ExampleInput
532 2 251 2 3 4 531 3 571 7 7 2 9 1 454 8 12 12 4Output
-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 
NoteIn 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].
532 2 251 2 3 4 531 3 571 7 7 2 9 1 454 8 12 12 4
-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  
['constructive algorithms', 'math', 'number theory', '*800']