A remote city has a park which contains zoo chain in it. The zoo chain containsr r zoos, labeled 1 through r. Bidirectional roads connect the zoos to form a simple cycle — a road connects zoos 1 and 2, zoos 2 and 3, and so on, and additionally a road connects zoos r and 1. The center of each zoo contains an identical animal, and all but one of the zoos has a beautiful animal having unique colour of skin currently living in the cage of that zoo. The remaining zoo holds only an empty cage.

The managers of the zoos want to rearrange the animals in a new order. To do this, they repeat the following process: First, they choose a zoo directly adjacent to the zoo containing an empty cage. Then, they very carefully and painstakingly carry the animal in this zoo across the adjoining road and place it in the empty cage.

You have to determine if it is possible for the managers of the zoos to arrange the animals in the desired order.

Input:
The first line contains a single integer - number of test cases.
For each test case the format of input is as follows:

1. The first line contains a single integer r — the total number of zoos.


2. The second line contains r space-separated integers p_i — the animal currently placed in the cage of i-th zoo. If p_i = 0, then the zoo has no animal. It is guaranteed that the p_i are distinct.


3. The third line contains r space-separated integers q_i — the desired animals of the ith zoo. Once again, q_i = 0 indicates the zoo desires no animal. It is guaranteed that the q_i are distinct.

Output:
For each test case print "YES" (without quotes) if the rearrangement can be done in the existing network, and "NO" otherwise in separate lines.

Constraints:
(1 ≤ T ≤ 100)
(2 ≤  r  ≤  200 000)
(0 ≤  p_i  < r )
(0 ≤  q_i < r )

Problem Setter: MAHIMA SINGH