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
from sys import stdin,stdout
from heapq import heapify,heappush,heappop,heappushpop
from collections import defaultdict as dd, deque as dq,Counter as C
from bisect import bisect_left as bl ,bisect_right as br
from itertools import combinations as cmb,permutations as pmb
from math import factorial as f ,ceil,gcd,sqrt,log,inf
mi = lambda : map(int,input().split())
ii = lambda: int(input())
li = lambda : list(map(int,input().split()))
mati = lambda  r : [ li() for _ in range(r)]
lcm = lambda a,b : (a*b)//gcd(a,b) 
MOD=10**9+7
def soe(n):
    prime = [True for i in range(n+1)]
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1
    return(prime)





def solve():
    n=ii()
    arr=li()
    p=[x for x in range(1,n+1)]
    m=arr.index(1)
    ans=False
    a,b=0,0
    cnt=1
    l=0
    while(a<=n):
        if arr[m]==cnt:
            l+=1
        cnt+=1
        a+=1
        m-=1
        if m==-1:
            m=n-1
    m=arr.index(1)
    cnt=1
    k=0
    while(b<=n):
        if arr[m]==cnt:
            k+=1
        cnt+=1
        b+=1
        m+=1
        if m==n:
            m=0
    if l==n or k==n:
        print("YES")
    else:
        print("NO")
for _ in range(ii()):
    solve()