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
array=[]
x=int(input())
for i in range(x):
    n =int(input())
    array =   [int(x) for x in input().split()]
    j=0
    for j in range(n):
        if 1 == array[j] :
        
            minIndex= j
            break
            
    m=0
    l=0
    if array[(minIndex+1)%n]==2:
     while(m<n-2):
        
        if array[(minIndex+1+m)%n]+1!=array[(minIndex+2+m)%n]:
            print("NO") 
            break
        else:
            if m==n-3:
               print("YES")
               m+=1
            else:
             
                m+=1
 
 
    elif array[(minIndex-1)]==2:
     while(m<n-2):
        
        if array[(minIndex-m-1)%n]+1!=array[(minIndex-2-m)%n]:
            print("NO") 
            break
        else:
            if l==n-3:
               print("YES")
               m+=1
            else:
             
                m+=1
    else:
        print('YES')