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
num = int(input())
first=[]
i=0
arr=[]
flag=0
size=0


while(i<num):
    size=int(input())
    arr=list(map(int,input().split()))
    if(size==1):
        print("YES")
    else:
        b=1
        anti=0
        clock=0
        n=len(arr)
        k=arr.index(b)
        j=arr.index(n)

        if(arr[j-1]==1):
            anti=1
        elif(arr[k-1]==n):
            clock=1
        #print(anti)
        #print(clock)
        if(anti ==1):
            p =1
            q = len(arr)
            low = arr.index(p)
            high = arr.index(q)
            if(arr[high-1] ==1):
                if(low==0 ):
                    anti=2

                while(low>0):
                    if(arr[low]+1==arr[low-1]):
                        anti=2
                        low=low-1
                    else:
                        anti=0
                        break;
                if(anti ==2):
                    while(high<=size-2):
                        if(arr[high]-1 == arr[high+1]):
                            anti=2
                            high=high+1
                        else:
                            anti=0
                            break
            else:
                anti=0
                break

        elif(clock==1):
            p=1
            q=len(arr)
            low=arr.index(p)
            high = arr.index(q)
            if(arr[low-1] == q):
                if(low==size-1):
                    clock=2
                else:
                    clock=0
                while(low<=size-2):
                    if(arr[low]+1 ==arr[low+1]):
                        clock=2
                        low=low+1
                    else:
                        clock=0
                        break
                if(clock==2):
                    while(high>0):
                        if(arr[high]-1==arr[high-1]):
                            clock=2
                            high=high-1
                        else:
                            clock=0
                            break
            else:
                clock=0
                break
        if(clock ==2 or anti==2):
            print("YES")
        else:
            print("NO")
    i=i+1
