C. Double Sort
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You 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
3
2
1 2
1 2
2
2 1
1 2
4
2 3 1 2
2 3 2 3
Output
0
-1
3
3 1
3 2
4 3