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.io.*;

public class B{
	public static boolean bwd(int[] arr, int pos)
	{
		int start = -1;
		if(pos==0)
		{
			start = arr.length-1;
		}
		else start = pos-1;
		int val = 2;
		for(int i=start;i!=pos;i--)
		{
			if(arr[i]!=val)
			{
				return false;
			}
			val++;
			if(i==0)
			{
				i = arr.length;
			}
		}
		return true;
	}
	public static boolean fwd(int[] arr, int pos)
	{
		int start = -1;
		if(pos==arr.length-1)
		{
			start = 0;
		}
		else start = pos+1;
		int val = 2;
		int n = arr.length;
		for(int i=start;i!=pos;)
		{
			if(arr[i]!=val)
			{
				return false;
			}
			val++;
			i = (i+1)%n;
		}
		return true;
	}
	
	public static void main(String[] args)
	{
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int t = fs.nextInt();
		for(int tt=0;tt<t;tt++)
		{
			int n = fs.nextInt();
			int[] arr = new int[n];
			int pos = -1;
			for(int i=0;i<n;i++)
			{
				arr[i] = fs.nextInt();
				if(arr[i]==1)
				{
					pos = i;
				}
			}
			boolean flag = true;
			if(fwd(arr,pos)==false && bwd(arr,pos)==false)flag = false;
			out.println(flag==true?"YES":"NO");
		}
		out.close();
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}


