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.

有 $n$ 名学生按某种顺序围成一个圆圈站立。第 $i$ 个位置上的学生的编号为 $p_i$。保证所有学生的编号均为 $1$ 到 $n$ 之间的互不相同的整数（即它们构成一个排列）。

学生们希望开始一场“环形舞”（round dance）。若在顺时针方向上，学生 $2$ 紧跟在学生 $1$ 之后（二者之间没有其他学生），学生 $3$ 紧跟在学生 $2$ 之后，……，学生 $n$ 紧跟在学生 $n-1$ 之后，则可以开始一场顺时针环形舞。而逆时针环形舞则几乎相同，唯一的区别是：对每个 $i$（从 $2$ 到 $n$），学生 $i$ 必须在逆时针方向上紧跟在学生 $i-1$ 之后。

例如，若学生编号按顺时针顺序排列为 $[2, 3, 4, 5, 1]$，则他们可以开始一场顺时针环形舞。若学生编号按顺时针顺序排列为 $[3, 2, 1, 4]$，则他们可以开始一场逆时针环形舞。

你的任务是判断是否可能开始一场环形舞。注意：在开始舞蹈前，学生不能改变自己的位置；他们既不能交换位置，也不能离开圆圈，也不允许其他学生加入圆圈。

你需要回答 $q$ 个相互独立的查询。

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).

输入的第一行包含一个整数 $q$（$1 \le q \le 200$），表示查询次数。随后是 $q$ 次查询。

每次查询的第一行包含一个整数 $n$（$1 \le n \le 200$），表示学生的数量。

每次查询的第二行包含一个索引的排列 $p_1, p_2, \dots, p_n$（$1 \le p_i \le n$），其中 $p_i$ 表示顺时针方向上第 $i$ 个学生的编号。保证所有 $p_i$ 均为 $1$ 到 $n$ 之间互不相同的整数（即构成一个排列）。

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".

对于每个查询，请输出其答案。如果能以给定的学生顺序开始圆圈舞，则输出 “YES”；否则输出 “NO”。