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
import sys
 
Lines = []
for Line in sys.stdin:
  Lines.append(Line.rstrip('\n'))
 
# Lines=["5",
# "4",
# "1 2 3 4",
# "3",
# "1 3 2",
# "5",
# "1 2 3 5 4",
# "1",
# "1",
# "5",
# "3 2 1 5 4"]

# Lines=["1",
# "4",
# "4 1 2 1"]
 
q = Lines[0]
q = int(q)
del(Lines[0])
for i in range(q):
   n = int(Lines[0])
   del(Lines[0])
 
   ind = Lines[0]
   del(Lines[0])
 
   ind = list(map(int,ind.split()))
   if (n==1):
     print("YES")
     continue
 
 
   index_1 = ind.index(1)
   m = max(ind)
   index_max = ind.index(max(ind))
   if (index_max==len(ind)-1)and(index_1==0):
      t= ind
   elif (index_1==len(ind)-1)and(index_max==0):  
      t= ind[::-1] 
   else:
      if index_max>index_1:
         t= ind[index_max:]+ind[:index_1+1]
         t = t[::-1]
      else:   
         t= ind[index_1:]+ind[:index_max+1]      

   if (t==sorted(ind))and(len(t)==n):
     print("YES")
   else:     
     print("NO")