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F. Swaps Again

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAyush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid.

Each test case consists of an integer $$$n$$$ and two arrays $$$a$$$ and $$$b$$$, of size $$$n$$$. If after some (possibly zero) operations described below, array $$$a$$$ can be transformed into array $$$b$$$, the input is said to be valid. Otherwise, it is invalid.

An operation on array $$$a$$$ is:

- select an integer $$$k$$$ $$$(1 \le k \le \lfloor\frac{n}{2}\rfloor)$$$
- swap the prefix of length $$$k$$$ with the suffix of length $$$k$$$

For example, if array $$$a$$$ initially is $$$\{1, 2, 3, 4, 5, 6\}$$$, after performing an operation with $$$k = 2$$$, it is transformed into $$$\{5, 6, 3, 4, 1, 2\}$$$.

Given the set of test cases, help them determine if each one is valid or invalid.

Input

The first line contains one integer $$$t$$$ $$$(1 \le t \le 500)$$$ — the number of test cases. The description of each test case is as follows.

The first line of each test case contains a single integer $$$n$$$ $$$(1 \le n \le 500)$$$ — the size of the arrays.

The second line of each test case contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ $$$(1 \le a_i \le 10^9)$$$ — elements of array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1$$$, $$$b_2$$$, ..., $$$b_n$$$ $$$(1 \le b_i \le 10^9)$$$ — elements of array $$$b$$$.

Output

For each test case, print "Yes" if the given input is valid. Otherwise print "No".

You may print the answer in any case.

Example

Input

5 2 1 2 2 1 3 1 2 3 1 2 3 3 1 2 4 1 3 4 4 1 2 3 2 3 1 2 2 3 1 2 3 1 3 2

Output

yes yes No yes No

Note

For the first test case, we can swap prefix $$$a[1:1]$$$ with suffix $$$a[2:2]$$$ to get $$$a=[2, 1]$$$.

For the second test case, $$$a$$$ is already equal to $$$b$$$.

For the third test case, it is impossible since we cannot obtain $$$3$$$ in $$$a$$$.

For the fourth test case, we can first swap prefix $$$a[1:1]$$$ with suffix $$$a[4:4]$$$ to obtain $$$a=[2, 2, 3, 1]$$$. Now we can swap prefix $$$a[1:2]$$$ with suffix $$$a[3:4]$$$ to obtain $$$a=[3, 1, 2, 2]$$$.

For the fifth test case, it is impossible to convert $$$a$$$ to $$$b$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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