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C. Double Sort

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given two arrays $$$a$$$ and $$$b$$$, both consisting of $$$n$$$ integers.

In one move, you can choose two indices $$$i$$$ and $$$j$$$ ($$$1 \le i, j \le n$$$; $$$i \neq j$$$) and swap $$$a_i$$$ with $$$a_j$$$ and $$$b_i$$$ with $$$b_j$$$. You have to perform the swap in both arrays.

You are allowed to perform at most $$$10^4$$$ moves (possibly, zero). Can you make both arrays sorted in a non-decreasing order at the end? If you can, print any sequence of moves that makes both arrays sorted.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of testcases.

The first line of each testcase contains a single integer $$$n$$$ ($$$2 \le n \le 100$$$) — the number of elements in both arrays.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$) — the first array.

The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le n$$$) — the second array.

Output

For each testcase, print the answer. If it's impossible to make both arrays sorted in a non-decreasing order in at most $$$10^4$$$ moves, print -1. Otherwise, first, print the number of moves $$$k$$$ $$$(0 \le k \le 10^4)$$$. Then print $$$i$$$ and $$$j$$$ for each move $$$(1 \le i, j \le n$$$; $$$i \neq j)$$$.

If there are multiple answers, then print any of them. You don't have to minimize the number of moves.

Example

Input

321 21 222 11 242 3 1 22 3 2 3

Output

0 -1 3 3 1 3 2 4 3

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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