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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int test = input.nextInt();
		while(test-->0){
		   int n = input.nextInt();
		   int arr[] = new int[n];
		   int index =-1;
		   for(int i =0;i<n;i++){
		       arr[i] =input.nextInt();
		       if(arr[i] == 1)index = i;
		   }
		   boolean ok = true;
		   int next = index == n-1?0 : index+1;
		   int val = 2;
		   while(next<n && index != next){
		        if(arr[next] != val){
		            ok = false;
		            break;
		        }else{val = val==n?1:val+1;}
		        if(next == n-1)next = -1;
		        next++;
		   }
		   if(ok){
		       System.out.println("YES");
		       continue;
		   }
		   next = index == 0?n-1:index-1;
		   val = 2;
		   ok = true;
		   while(next>=0 && index != next){
		       if(arr[next] != val){
		           ok = false;
		           break;
		       }else{
		           val = val == n?1:val+1;
		       }
		       if(next == 0)next =n;
		       next--;
		   }
		   if(ok)System.out.println("YES");
		   else System.out.println("NO");
		   
		   
		}
	}
}
