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.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) 
	{	

		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		
		while(t-->0)
		{
			int n=sc.nextInt();
			ArrayList<Integer> al=new ArrayList<>();
			
			for(int i=0;i<n;i++)
			{
				int x=sc.nextInt();
				al.add(x);
			}
			
			if(n<4)
				System.out.println("YES");
			else
			{
				
				boolean flagT=al.get(0)<al.get(1)?(al.get(1)<al.get(2)):(al.get(1)<al.get(2));  //true=inc  false=desc
				
				int i;
				int temp=al.get(0);
				for(i=1;i<n;i++)
				{
					if(flagT)
					{
						if(temp>al.get(i))
							break;
						else
							temp=al.get(i);
					}
					else
					{
						if(temp<al.get(i))
							break;
						else
							temp=al.get(i);
					}
				}
				
				if(flagT)
				{
					int start=i;
					int end=n-1;
					while(start<=end)
					{
						int a=al.get(start);
						al.set(start, al.get(end));
						al.set(end, a);
						start++;
						end--;
					}
				}
				else
				{
					int start=i;
					int end=n-1;
					while(start<=end)
					{
						int a=al.get(start);
						al.set(start, al.get(end));
						al.set(end, a);
						start++;
						end--;
					}
					
					start=0;
					end=i-1;
					while(start<=end)
					{
						int a=al.get(start);
						al.set(start, al.get(end));
						al.set(end, a);
						start++;
						end--;
					}
				
				}
				
				
				int x=al.get(0);
				boolean flag=false;
				
				for(int j=1;j<n;j++)
				{
				  if(x>al.get(j))
				  {
					flag=true;
					break;
				  }
				  else
					  x=al.get(j);
				}
				
				if(flag)
					System.out.println("NO");
				else
					System.out.println("YES");
			 }
			}
		}
}
