A12832 | 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".