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
queryTot = int(input())
out="";
for queryIndex in range(queryTot):

    # Get the number of students, n, and the sequence of students, query  
    n = int(input())
    queryInp = input()

    # Turn query from a sting to an integer list, and find where n is in the query, nIndex
    query = [int(elem) for elem in queryInp.split(" ")]
    nIndex = query.index(n)
    
    # Trivial cases as all sequences for n=1,2,3 are passable
    if n in (1,2,3):
        out = out+"YES\n"

    # Check first two numbers to see how to check rest of numbers
    elif (query[1]==query[0]+1) or (nIndex==0 and query[1]==1):
        #Increment all elements past nIndex by n, and check if the diff between elements is all 1 
        replace = [elem+n for elem in query[nIndex+1:]]
        query[nIndex+1:]=replace;
        queryDiff = [fin-init for init, fin in zip(query[:-1], query[1:])]
        if all([elem==1 for elem in queryDiff]):
            out = out+"YES\n"
        else:
            out = out+"NO\n"
    elif (query[1]==query[0]-1) or (nIndex==1 and query[0]==1):
        #Increment all elements before nIndex by n, and check if the diff between elements is all -1 
        replace = [elem+n for elem in query[:nIndex]]
        query[:nIndex]=replace;
        queryDiff = [fin-init for init, fin in zip(query[:-1], query[1:])]
        if all([elem==-1 for elem in queryDiff]):
            out = out+"YES\n"
        else:
            out = out+"NO\n"

    # If condition wasnt met then sequence doesn't pass  
    else:
        
        out = out+"NO\n"
# Remove last new line character and print results
cleaned =out.rstrip()
print(cleaned)
