I. FST: First Search Traversal
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

As her assignment, Riri's given two permutations$$$^{\text{∗}}$$$ of length $$$n$$$. Determine if there exists a rooted tree such that the first permutation is one of its DFS orders and the second permutation is one of its BFS orders.

As a reminder, the DFS order is generated by the following pseudocode:

dfs_order = []

def dfs(v):
    dfs_order.append(v)
    pick an arbitrary permutation s of children of v
    for child in s:
        dfs(child)

dfs(root)

and the BFS order is generated by the following pseudocode:

bfs_order = []
queue = [root]
while len(queue):
    u = queue[0]
    bfs_order.append(u)
    queue = queue[1:]
    pick an arbitrary permutation s of children of u
    for child in s:
        queue.append(child)

However, Riri is addicted to kemurikusa and is not interested in these boring assignment, so she forwards the assignment to you. Can you do it well?

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$1\le n\le 2\cdot10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\dots,a_n$$$ ($$$1\le a_i\le n$$$, $$$a_i\neq a_j$$$) — the first permutation.

The third line of each test case contains $$$n$$$ integers $$$b_1,b_2,\dots,b_n$$$ ($$$1\le b_i\le n$$$, $$$b_i\neq b_j$$$) — the second permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, output "YES" if such a tree exists; otherwise, output "NO". You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Example
Input
2
2
1 2
1 2
2
1 2
2 1
Output
YES
NO