Circle of Students

## 题目描述 有 $n$ 个学生按一定的顺序围成一圈，每个学生有一个互不相同的编号 $p_i$ 。 现在这些学生围成一圈跳圆圈舞，他们可以按顺时针或逆时针跳舞，但必须满足以下条件之一：\ 1、编号为 $2$ 的学生是编号为 $1$ 的学生的**顺**时针顺序的第一个学生，编号为 $3$ 的学生是编号为 $2$ 的学生的**顺**时针顺序的第一个学生，以此类推。\ 2、编号为 $2$ 的学生是编号为 $1$ 的学生的**逆**时针顺序的第一个学生，编号为 $3$ 的学生是编号为 $2$ 的学生的**逆**时针顺序的第一个学生，以此类推。 例如：如果有 $5$ 个学生，按**顺**时针顺序排列的学生的 $p_i$ 为$[2,3,4,5,1]$ ，那就**顺**时针跳舞；如果有 $4$ 个学生，按**顺**时针顺序排列的学生的 $p_i$ 为$[3,2,1,4]$ ，那就**逆**时针跳舞。 一共有 $q$ 组询问。 ## 输入格式 第一行输入一个正整数 $q$ ，表示有 $q$ 组询问。\ 每组询问分为两行：\ 第一行输入一个正整数 $n$ ，表示有 $n$ 个学生。\ 第二行输入一行正整数 $p_i$ ，表示按顺时针排列的学生的编号。 ## 输出格式 输出共 $q$ 行。\ 每一行输出一组询问的答案，如果他们能按顺时针或逆时针跳舞，则输出"YES"；否则输出"NO"。 ## 数据范围 $1\leq n,q\leq 200$\ $1\leq p_i\leq n$

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".

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

YES
YES
NO
YES
YES