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
//Circle of students
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.StringTokenizer;
public class CircleOfStudents
{
	public static void main(String args[]) throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0)
		{
			int n = Integer.parseInt(br.readLine());
			int a[] = new int[n];
			int pos = 0;
			boolean isIncreasing = false, isDecreasing = false;
			StringTokenizer st = new StringTokenizer(br.readLine());
			for(int i = 0; i < n; i++)
			{
				a[i] = Integer.parseInt(st.nextToken());
				if(a[i] == 1)
					pos = i;
			}
			if(n == 1)
			{
				System.out.println("YES");
				continue;
			}
			if(pos == 0 || pos == n-1 || pos == n-2)
			{
				for(int i = 0; i < n-1; i++)
				{
					if(a[i] != 1 && a[i+1] != 1)
					{
						if(a[i+1]-a[i] == 1)
							isIncreasing = true;
						else
						{
							isIncreasing = false;
							break;
						}
					}
				}
				if(isIncreasing)
					System.out.println("YES");
				else
				{
					for(int i = 0; i < n-1; i++)
					{
						if(a[i] != 1 && a[i+1] != 1)
						{
							if(a[i]-a[i+1] == 1)
								isDecreasing = true;
							else
							{
								isDecreasing = false;
								break;
							}
						}
					}
					System.out.println(isDecreasing ? "YES" : "NO");
				}
			}
			else
			{
				for(int i = 0; i < pos-1; i++)
				{
					if(a[i+1]-a[i] == 1)
						isIncreasing = true;
					else if(a[i]-a[i+1] == 1)
						isDecreasing = true;
				}
				if(isIncreasing && !isDecreasing) 
				{
					for(int i = pos+1; i < n-1; i++)
					{
						if(a[i+1]-a[i] == 1)
							isIncreasing = true;
						else
							isIncreasing = false;
					}
					System.out.println(isIncreasing ? "YES" : "NO");
				}
				else if(isDecreasing && !isIncreasing)
				{
					for(int i = pos+1; i < n-1; i++)
					{
						if(a[i]-a[i+1] == 1)
							isDecreasing = true;
						else
							isDecreasing = false;
					}
					System.out.println(isDecreasing ? "YES" : "NO");
				}
				else
					System.out.println("NO");
			}
		}
	}
}