Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Circle of Students

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ students standing in a circle in some order. The index of the $$$i$$$-th student is $$$p_i$$$. It is guaranteed that all indices of students are distinct integers from $$$1$$$ to $$$n$$$ (i. e. they form a permutation).

Students want to start a round dance. A clockwise round dance can be started if the student $$$2$$$ comes right after the student $$$1$$$ in clockwise order (there are no students between them), the student $$$3$$$ comes right after the student $$$2$$$ in clockwise order, and so on, and the student $$$n$$$ comes right after the student $$$n - 1$$$ in clockwise order. A counterclockwise round dance is almost the same thing — the only difference is that the student $$$i$$$ should be right after the student $$$i - 1$$$ in counterclockwise order (this condition should be met for every $$$i$$$ from $$$2$$$ to $$$n$$$).

For example, if the indices of students listed in clockwise order are $$$[2, 3, 4, 5, 1]$$$, then they can start a clockwise round dance. If the students have indices $$$[3, 2, 1, 4]$$$ in clockwise order, then they can start a counterclockwise round dance.

Your task is to determine whether it is possible to start a round dance. Note that the students cannot change their positions before starting the dance; they cannot swap or leave the circle, and no other student can enter the circle.

You have to answer $$$q$$$ independent queries.

Input

The first line of the input contains one integer $$$q$$$ ($$$1 \le q \le 200$$$) — the number of queries. Then $$$q$$$ queries follow.

The first line of the query contains one integer $$$n$$$ ($$$1 \le n \le 200$$$) — the number of students.

The second line of the query contains a permutation of indices $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$), where $$$p_i$$$ is the index of the $$$i$$$-th student (in clockwise order). It is guaranteed that all $$$p_i$$$ are distinct integers from $$$1$$$ to $$$n$$$ (i. e. they form a permutation).

Output

For each query, print the answer on it. If a round dance can be started with the given order of students, print "YES". Otherwise print "NO".

Example

Input

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

Output

YES YES NO YES YES

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/07/2020 00:54:16 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|