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
{
    
        public static void main(String args[])throws IOException
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int t=Integer.parseInt(br.readLine());
            for(int i=0; i<t;i++)
            {
             int n=Integer.parseInt(br.readLine());
             int arr[]=new int[n];
             String str=br.readLine();
             StringTokenizer st=new StringTokenizer(str," ");
             for(int j=0; j<n; j++)
             { 
             	arr[j]=Integer.parseInt(st.nextToken());
             }
             if(check(arr))
             {
             	System.out.println("yes");
             }
             else
             System.out.println("no");
             
              
            }
        }
        public static boolean check(int brr[])
        { int l=brr.length; int c=0; int d=0;
        for(int i=0; i<l-1; i++)
        {
        	if(brr[i]==(brr[i+1]+1))
        	c++;
        	else if
        	(brr[i]==(brr[i+1]-1))
        	d++;
        }
        if(c>=(l-2)||d>=(l-2))
        
     	return true;
        	
        else
        return false;
        
        
        
       
       } 
    }
    
    

