CF1203A Circle of Students

There 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.

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).

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".