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
def Is_Possible(l, index, inc):
    new_l = []
    count = len(l)
    while(count != 0):
        count -= 1
        new_l.append(l[index])
        index = index + inc
        if(index == -1):
            index = len(l)-1
        elif(index == len(l)):
            index = 0
    if(new_l == sorted(l)):
        return("YES")
    else:
        return("NO")
q = int(input()) #taking input of number of queries
if((q < 1) or (q > 200)):
    print("NO")
else:
    for h in range(0, q, +1):
        n = int(input())
        if((n < 1) or (n > 200)):
            print("NO")
        else:
            l = input()
            l = l.split(" ")
            if(len(l) != n):
                print("NO")
            else:
                count_greater_number = 0
                for i in range(0, len(l), +1):
                    l[i] = int(l[i])
                    if((l[i] > n) or (l[i] < 1)):
                        count_greater_number += 1
                if(count_greater_number > 0):
                    print("NO")
                else:
                    if((len(l) == 1) and (l[0] == 1)):
                        print("YES")
                    else:
                        check_l = []
                        check_l = sorted(l)
                        for i in range(0, len(check_l), +1):
                            if(i+1 != check_l[i]):
                                print("NO")
                                break
                        index = l.index(1)
                        if(index == 0):
                            if(l[index+1] == 2):
                                print(Is_Possible(l, index, +1))
                            elif(l[index-1] == 2):
                                print(Is_Possible(l, index, -1))
                            else:
                                print("NO")
                        elif(index == len(l)-1):
                            if(l[0] == 2):
                                print(Is_Possible(l, index, +1))
                            elif(l[index-1] == 2):
                                print(Is_Possible(l, index, -1))
                            else:
                                print("NO")
                        elif(0 < index < len(l)-1):
                            if(l[index+1] == 2):
                                print(Is_Possible(l, index, +1))
                            elif(l[index-1] == 2):
                                print(Is_Possible(l, index, -1))
                            else:
                                print("NO")