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 Check (students,size):
    minimum = min(students);
    # Only one student
    if size ==  1:
        print 'YES'
    # More than one student 
    # Checking for clock_wise - see if we have an ascending order at the beginning
    elif students[1] - students[0] == 1:
        students_2 = []; students_2.extend(students); students_2.sort()
        # Check if we have a complete ascending order (clockwise motion realized)
        if students ==  students_2:
            print 'YES'
        else:
            Fault = False
            for i in range (1,size):
                # stop when limit is reached
                if i + 1 < size:
                    if students[i + 1] - students[i] == 1:
                        pass
                    elif students[i+1] == minimum:
                        if abs(students[i+1] -  students[i]) == size - 1:
                            pass
                        else:
                            Fault = True
                            break
                    else:
                        Fault = True
                        break
            if Fault:
                print 'NO'
            else:
                print 'YES'
    elif abs(students[0] - students[-1]) == 1:
        Fault2 = False
        # Start the anticlockwise 
        rev_students = students[::-1]
        for j in range(size):
            if j+1 < size:
                if abs(rev_students[j] - rev_students[j+1]) == 1:
                    pass
                elif rev_students[j] == minimum or rev_students[j+1] == minimum:
                    if abs(rev_students[j] - rev_students[j+1]) == size -1:
                        pass 
                    else:
                        Fault2 = True
                        break
                else:
                    Fault2= True
                    break
        if Fault2:
            print 'NO'
        else:
            print 'YES'
    
    else:
        print 'NO'
queries = input()
for i in range(queries):
    size = input(); students = list(map(int,raw_input().split()))
    Check(students,size)
