1203_A. Circle of Students
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
```python
t=int(input())
while t:
	n=int(input())
	a=list(map(int,input().split()))
	b=[0]*n
	for i in range(n):
		b[a[i]-1]=i+1
	k=0
	flag=0
	# print(b)
	if n==1:
		print("YES")
	elif abs(b[0]-b[1])==1 or abs(b[0]-b[1])==n-1:
		if abs(b[0]-b[1])==1:
			k=b[0]-b[1]
		else:
			k=b[1]-b[2]
		for j in range(1,n):
			if j==n-1:
				if b[j]-b[0]==k or abs(b[j]-b[0])==n-1:
					print("YES")
			else:
				if b[j]-b[j+1]!=k and abs(b[j]-b[j+1])!=n-1:
					flag=1
					break
		if flag:
			print("NO")
	else:
		print("NO")
	t-=1
```