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.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 200) — the number of queries. Then q queries follow.

The first line of the query contains one integer n (1 ≤ n ≤ 200) — the number of students.

The second line of the query contains a permutation of indices p_1, p_2, ..., p_n (1 ≤ p_i ≤ 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).

Output

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".

Example

Input


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
read_int = lambda: int(input())
read_ints = lambda: list(map(int, input().split(' ')))


def solve(n, nums):
    if len(nums) <= 3:
        return 'YES'

    less = True if nums[0] > nums[1] else False
    changed = False
    i = 1
    if less:
        for x in range(1, len(nums)):
            if nums[x] != nums[x - 1] - 1:
                changed = True
                i = x
                break

        if changed:
            for x in range(i + 1, len(nums)):
                if nums[x] != nums[x - 1] - 1:
                    return 'NO'
    else:
        for x in range(1, len(nums)):
            if nums[x] != nums[x - 1] + 1:
                changed = True
                i = x
                break

        if changed:
            for x in range(i + 1, len(nums)):
                if nums[x] != nums[x - 1] + 1:
                    return 'NO'

    return 'YES'


#
# def solve2(n, nums):
#     if len(nums) <= 3:
#         return 'YES'
#
#     cnext = lambda i: i % n
#     change = 0
#     for i in range(1, len(nums)):
#         if abs(nums[i] - nums[i - 1]) != 1:
#             change = i
#
#     if
#     for _ in range(n):


if __name__ == '__main__':
    T = read_int()
    for i in range(T):
        n = read_int()
        nums = read_ints()
        result = solve(n, nums)
        print(result, end='' if i == T - 1 else '\n')
