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
#Problem is: Circle of students
stored_values=[]
number_of_queries=int(input())
for i in range(number_of_queries):
    
  number_of_students=int(input())
  permutations_of_students=input().split()
  
  #converts the list of strings to a list of ints
  for i in range(number_of_students):
    permutations_of_students[i]=int(permutations_of_students[i])
    
  one_starts_at=permutations_of_students.index(1)


  #checks if they are clock-wise or anti-clockwise
  forward_works = "YES"
  backward_works = "YES"

  for i in range(number_of_students - 1):
      forward_index = (one_starts_at+i+1)%number_of_students
      backward_index = (one_starts_at-i-1)%number_of_students
      if not(permutations_of_students[forward_index]==i+2):
        forward_works="NO"
      if not(permutations_of_students[backward_index]==i+2):
        backward_works="NO"

  if (forward_works == "YES" or backward_works == "YES"):
    print ("YES")
  else:
    print ("NO")
    

    
    
    
  
  

	 		    		 		 	  	 		     	 		