# Circle of Students

## 题意翻译

## 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 $1\leq n,q\leq 200$\ $1\leq p_i\leq n$

## 题目描述

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.

## 输入输出格式

### 输入格式

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).

### 输出格式

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".

## 输入输出样例

### 输入样例 #1

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


### 输出样例 #1

YES
YES
NO
YES
YES