A. Circle of Studentstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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).OutputFor 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".ExampleInput
5
4
1 2 3 4
3
1 3 2
5
1 2 3 5 4
1
1
5
3 2 1 5 4
Output
YES
YES
NO
YES
YES

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 
['implementation', '*1000']