Swaps Again
Description
Ayush, 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.
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 $b$.
For each test case, print "Yes" if the given input is valid. Otherwise print "No".
You may print the answer in any case.
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.
Samples
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
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 $b$.