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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;
 
public class myFile
{
	public static void main(String args[])
	{
	   Scanner sc = new Scanner(System.in);
	   int test,n,index,x;
	   test  = sc.nextInt();
	   List<Integer> arrList = new ArrayList<Integer>();
	   List<Integer> split1 = new ArrayList<Integer>();
	   List<Integer> split2 = new ArrayList<Integer>();
	   Set<Integer> difference = new HashSet<Integer>();
	   while(test>0 && sc.hasNextInt())
	   {
		  index =0;
		  test--;
		  n = sc.nextInt();
		  arrList.clear();
		  split1.clear();
		  split2.clear();
		  difference.clear();
		  for(int i=0;i<n;i++)
		  {
			  x = sc.nextInt();
			  if(x==1)
			  {
				  index = i;
			  }
			  arrList.add(x);
		  }
		  for(int i=0;i<index;i++)
		  {
			  split1.add(arrList.get(i));
		  }
		  for(int i=index+1;i<n;i++)
		  {
			  split2.add(arrList.get(i));
		  }
		  
		  for(int i=1;i<split1.size();i++)
		  {
			  int diff = split1.get(i)-split1.get(i-1);
			  difference.add(diff);
		  }
		  for(int i=1;i<split2.size();i++)
		  {
			  int diff = split2.get(i)-split2.get(i-1);
			  difference.add(diff);
		  }
		  if(difference.size()<2)
			  System.out.println("YES");
		  else
			  System.out.println("NO");
	   }
	}

 
}