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.*;
import java.lang.*;

public class Cf183
{
	public static void main(String args[])
	{
		Scanner in = new Scanner(System.in);
		int q = in.nextInt();
		read:
		while(q-->0)
		{
			int n = in.nextInt();
			int arr[] = new int[4*n];
			int i,j,k;
			for(i=0;i<n;i++)
			{
				arr[i] = in.nextInt();
			}
			if(n==1)
			{
				System.out.println("YES");
				continue read;
			}
			int d = 0;
			for(i=0;i<n;i++)
			{
				if(i==1)
				{
					if(arr[0] != 1 && arr[0] != n)
					{
						d = arr[1]-arr[0];
						if(d>1 || d <-1)
						{
							System.out.println("NO");
							continue read;
						}
					}
					else if(arr[0] ==1)
					{
						if(arr[1]==2)
							d=1;
						else if(arr[1] == n)
							d = -1;
						else
						{
							System.out.println("NO");
							continue read;
						}
					}
					else if(arr[0]==n)
					{
						if(arr[1]==1)
							d =1;
						else if(arr[1]==n-1)
							d = -1;
						else
						{
							System.out.println("NO");
							continue read;
						}
					}
				}            
				else if(d ==1 )
				{ 
					int t=0;
					if(arr[i] ==1)
						t = arr[i] - arr[i-1]%n;
					else
						t = arr[i] -arr[i-1];
					if(t != d)
					{
						System.out.println("NO");
						continue read;
					}
				}
				else if(d ==-1)
				{
					int t=0;
					if(arr[i] ==n)
						t = arr[i]%n - arr[i-1];
					else
						t = arr[i] -arr[i-1];
					if(t != d)
					{
						System.out.println("NO");
						continue read;
					}
				}
			}
			System.out.println("YES");
		}
	}
}