Codeforces Round 922 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

constructive algorithms

data structures

greedy

implementation

sortings

*900

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Minimize Inversions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$(3,4)$$$).

Input

The 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 $$$2\cdot10^5$$$.

Output

For 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.

Example

Input

351 2 3 4 55 4 3 2 133 1 23 1 262 5 6 1 3 41 5 3 6 2 4

Output

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

Note

In 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 $$$7$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/13/2024 04:18:17 (j2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|