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
#!/usr/bin/python3

from collections import *
from inspect import currentframe
from math import *
from sys import stdin, stdout, stderr


def main():
    oo = 0x3f3f3f3f3f3f3f3f
    eps = 1e-9

    def TR(n):
        """n: String, name of the variable to track"""
        if False:
            x = currentframe().f_back.f_locals[n]
            stderr.write("{} = {}\n".format(n, x))

    ddict = defaultdict
    rl = stdin.readline
    rc = stdin.read
    wr = stdout.write

    q = int(rl())
    for i in range(q):
        l = int(rl())
        stu = list(map(int, rl().split()))

        TR("l")
        TR("stu")

        if l in [1, 2]:
            wr("YES\n")
            continue

        m = stu.index(max(stu))
        TR("m")
        d = stu[(m+1)%l]-stu[m]
        if d not in [-1, 1]:
            d = stu[m]-stu[(m-1)%l]

        if d not in [-1, 1]:
            wr("NO\n")
            continue

        TR("d")
        if d  == 1:
            m = (m+1)%l
        answer = True
        for i in range(l-1):
            if stu[(m+i+1)%l] - stu[(m+i)%l] != d:
                TR("i")
                answer = False
                break


        wr("YES\n") if answer else wr("NO\n")


main()
