D. Cyclic Rotation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is an array $$$a$$$ of length $$$n$$$. You may perform the following operation any number of times:

  • Choose two indices $$$l$$$ and $$$r$$$ where $$$1 \le l < r \le n$$$ and $$$a_l = a_r$$$. Then, set $$$a[l \ldots r] = [a_{l+1}, a_{l+2}, \ldots, a_r, a_l]$$$.

You are also given another array $$$b$$$ of length $$$n$$$ which is a permutation of $$$a$$$. Determine whether it is possible to transform array $$$a$$$ into an array $$$b$$$ using the above operation some number of times.

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$)  — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10 ^ 5$$$)  — the length of array $$$a$$$ and $$$b$$$.

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

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

It is guaranteed that $$$b$$$ is a permutation of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10 ^ 5$$$

Output

For each test case, print "YES" (without quotes) if it is possible to transform array $$$a$$$ to $$$b$$$, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Example
Input
5
5
1 2 3 3 2
1 3 3 2 2
5
1 2 4 2 1
4 2 2 1 1
5
2 4 5 5 2
2 2 4 5 5
3
1 2 3
1 2 3
3
1 1 2
2 1 1
Output
YES
YES
NO
YES
NO
Note

In the first test case, we can choose $$$l=2$$$ and $$$r=5$$$ to form $$$[1, 3, 3, 2, 2]$$$.

In the second test case, we can choose $$$l=2$$$ and $$$r=4$$$ to form $$$[1, 4, 2, 2, 1]$$$. Then, we can choose $$$l=1$$$ and $$$r=5$$$ to form $$$[4, 2, 2, 1, 1]$$$.

In the third test case, it can be proven that it is not possible to transform array $$$a$$$ to $$$b$$$ using the operation.