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
q = int(input())
n = []
table_pos = []


for i in range(q):
    n.append(int(input()))
    table_pos.append(list(map(int , input().split())))
    
for j in range(q):
    Check_clock = 1
    Check_anticlock = 1 
    temp = 1
    count = n[j]
    table = table_pos[j]
    x = table.index(1)
    if(x == count-1):
        for v in range(x):
            if(table[v]-table[v+1] != 1):
                Check_anticlock = 0
                break
    else:
            
        for k in range(x,count-1):
            if(table[k+1]-table[k] != 1):
                Check_clock = 0
            if(k != x and table[k]-table[k+1] != 1):
                Check_anticlock = 0
        
    if(Check_clock !=0 and x !=0 ):
        if(table[0]-table[count-1] != 1):
            Check_clock = 0
        else:
            for g in range(x-1):
                if(table[g+1]-table[g] != 1):
                    Check_clock = 0
                    break
    if(Check_anticlock != 0 and x!=0):
        if(x!= count-1 and table[count-1]-table[0] != 1):
            Check_anticlock = 0
            
        else:
            for h in  range(x-1):
                if(table[h]-table[h+1] != 1):
                    Check_anticlock = 0
                    break
                    
    if(Check_clock == 1 or Check_anticlock == 1):
        print("YES")
        temp = 0
        
    if(temp == 1):
        print("NO")
        
        
         
        
        
    
