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.io.*;
import java.util.*;
public class Main {
	static BufferedReader br;
	static PrintWriter pr;
	static int cin() throws Exception
	{
		return Integer.valueOf(br.readLine());
	}
	static int[] split() throws Exception
	{
		String[] cmd=br.readLine().split(" ");
		int[] ans=new int[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Integer.valueOf(cmd[i]);
		}
		return ans;
	}
	static long[] splitL() throws IOException
	{
		String[] cmd=br.readLine().split(" ");
		long[] ans=new long[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Long.valueOf(cmd[i]);
		}
		return ans;
	}
	static int sum(long n)
	{
		int ans=0;
		while(n!=0)
		{
			ans=ans+(int)(n%10);
			n=n/10;
		}
		return ans;
	}
	static int gcd(int x,int y)
	{
		if(x==0)
			return y;
		if(y==0)
			return x;
		if(x>y)
			return gcd(x%y,y);
		else
			return gcd(x,y%x);
	}
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		br=new BufferedReader(new InputStreamReader(System.in));
		pr=new PrintWriter(new OutputStreamWriter(System.out));
		int cases=cin();
		while(cases!=0)
		{
			cases--;
			int n=cin();
			int[]arr=split();
			int[]dup=new int[2*n];
			for(int i=0;i<n;i++)
			{
				dup[i]=dup[i+n]=arr[i];
			}
			boolean b=false;
			for(int i=0;i<2*n;i++)
			{
				if(dup[i]==1)
				{
					boolean g=true;
					for(int j=i;j<(i+n);j++)
					{
						if(j>=2*n || dup[j]!=(dup[i]+j-i))
						{
							g=false;
							break;
						}
					}
					if(g)
					{
						b=true;
						break;
					}
				}
			}
			for(int i=0;i<2*n;i++)
			{
				if(dup[i]==n)
				{
					boolean g=true;
					for(int j=i;j<(i+n);j++)
					{
						if(j>=2*n || dup[j]!=(dup[i]-j+i))
						{
							g=false;
							break;
						}
					}
					if(g)
					{
						b=true;
						break;
					}
				}
			}
			if(b)
				System.out.println("YES");
			else
				System.out.println("NO");
		}
	}
}
