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.*;
import java.lang.*;
import java.math.*;
public class CodeChef
{
	static int binarySearch(int arr[], int n)
	{
		int left=0;
		int right=arr.length-1;
		while(left<=right)
		{
			int mid = (left+right)/2;
//			System.out.println("Value of mid is "+mid+" "+left+" "+right);
			if(arr[mid]==n) return mid;
			if(arr[0]<=arr[mid])
			{
				if(n<arr[mid] && n>=arr[0]) {  right=mid-1; }
				else {  left=mid+1; }
			}
			else
			{
				if(n>arr[mid] && n<=arr[arr.length-1]) left=mid+1;
				else right=mid-1;
			}
		}
		return -1;
	}
	static boolean check(int arr[], int index)
	{
		ArrayList<Integer> list = new ArrayList<Integer>();
		for(int i=index; i>=0; i--) list.add(arr[i]);
		for(int i=arr.length-1; i>index; i--) list.add(arr[i]);
			ArrayList<Integer> list2 = new ArrayList<Integer>();
			for(int i=index; i<arr.length; i++) list2.add(arr[i]);
			for(int i=0; i<index; i++) list2.add(arr[i]);
		if(list.size()==1)
		{
			if(list.get(0)==1) return true;
			else return false;
		}
		if(list.get(0)==1 && list.get(1)==2)
		{
			for(int i=1; i<list.size(); i++)
				if(list.get(i)-list.get(i-1)!=1) return false;
			return true;
		}
		else if(list2.get(0)==1 && list2.get(1)==2)
		{
			for(int i=1; i<list2.size(); i++)
				if(list2.get(i)-list2.get(i-1)!=1)return false;
			return true;
		}
		return false;
	}
	public static void main(String[] args) throws IOException
	{
		Scanner scan = new Scanner(System.in);
		int testcases = scan.nextInt();
		for(int m=0; m<testcases; m++)
		{
		  int n = scan.nextInt();
		  int arr[] = new int[n];
		  for(int i=0; i<n; i++)
		  {
			  arr[i]=scan.nextInt();
		  }
		  int index = binarySearch(arr,1);
//		  System.out.println("Index"+ index);
		  boolean bool=false;
		  if(index!=-1)
		  bool = check(arr,index);
		  System.out.println(bool ? "YES": "NO");
		}
   	}
}