Preparando MOJI
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
Informação
Provedor Codeforces
Código CF1203A
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Datas 09/05/2023 09:50:36
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