B. Minimize Inversionstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two permutations a and b of length n. A permutation is an array of n elements from 1 to n where all elements are distinct. For example, an array [2,1,3] is a permutation, but [0,1] and [1,3,1] aren't.You can (as many times as you want) choose two indices i and j, then swap a_i with a_j and b_i with b_j simultaneously. You hate inversions, so you want to minimize the total number of inversions in both permutations.An inversion in a permutation p is a pair of indices (i, j) such that i < j and p_i > p_j. For example, if p=[3,1,4,2,5] then there are 3 inversions in it (the pairs of indices are (1,2), (1,4) and (3,4)).InputThe first line contains an integer t (1 \leq t \leq 20\,000) — the number of test cases.Each test case consists of three lines. The first line contains an integer n (1 \leq n \leq 2\cdot10^5) — the length of the permutations a and b. The second line contains n integers a_1, a_2, \ldots, a_n (1 \leq a_i \leq n) — permutation a. The third line contains b in a similar format. It is guaranteed that the sum of n over all test cases does not exceed 2\cdot10^5.OutputFor each test case, output two permutations a' and b' (in the same format as in the input) — the permutations after all operations. The total number of inversions in a' and b' should be the minimum possible among all pairs of permutations that can be obtained using operations from the statement.If there are multiple solutions, print any of them.ExampleInput
351 2 3 4 55 4 3 2 133 1 23 1 262 5 6 1 3 41 5 3 6 2 4Output
3 2 5 1 4
3 4 1 5 2
1 2 3
1 2 3
2 3 4 6 5 1
1 2 4 3 5 6
NoteIn the first test case, the minimum possible number of inversions is 10.In the second test case, we can sort both permutations at the same time. For this, the following operations can be done:  Swap the elements in the positions 1 and 3 in both permutations. After the operation, a = [2,1,3], b = [2,1,3].  Swap the elements in the positions 1 and 2. After the operations, a and b are sorted. In the third test case, the minimum possible number of inversions is 7.
351 2 3 4 55 4 3 2 133 1 23 1 262 5 6 1 3 41 5 3 6 2 4
3 2 5 1 4 3 4 1 5 2 1 2 3 1 2 3 2 3 4 6 5 1 1 2 4 3 5 6 
['constructive algorithms', 'data structures', 'greedy', 'implementation', 'sortings', '*900']