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 java.util.*;
public class CIRCLE
{
    public static void main(String[] args)
    {
        try
        {
            Scanner sc=new Scanner(System.in);
            int T=sc.nextInt();
            for(int j=0;j<T;j++)
            {
                int i,in=0,a=2,t=1,inn;
                int N=sc.nextInt();
                int C[]=new int[N];
                for(i=0;i<N;i++)
                {
                    C[i]=sc.nextInt();
                    if(C[i]==1)
                        in=i;
                }
                if(in+1==N)
                    inn=0;
                else
                    inn=in+1;
                if(N>1&&C[inn]==2)
                {
                    for(i=2;i<=N;i++)
                    {
                        if(C[inn]==i)
                        {
                            inn++;
                            if(inn==N)
                                inn=0;
                        }
                        else
                        {
                            t=0;
                            break;
                        }
                    }
                }
                if(in==0)
                    inn=N-1;
                else
                    inn=in-1;
                if(N>1&&C[inn]==2)
                {
                    for(i=2;i<=N;i++)
                    {
                        if(C[inn]==i)
                        {
                            inn--;
                            if(inn==-1)
                                inn=N-1;
                         }
                        else
                        {
                            t=0;
                            break;
                        }
                    }
                }
                if(N==1&&C[0]==1)
                {
                    System.out.println("YES");
                }
                if(N==1&&C[0]!=1)
                {
                    System.out.println("NO");
                }
                else if(t==0)
                {
                    System.out.println("NO");
                }
                else
                {
                    System.out.println("YES");
                }
            }
        }
        catch(Exception e)
        {
            System.exit(0);
        }
    }
}