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.Scanner;
public class Circle_of_Students{

    public static void main(String[] args) 
    {
       int t,i,j;
       int n;
       int c=0,jj=0;
       Scanner in = new Scanner(System.in);
       t=in.nextInt();
       for(i=0;i<t;i++)
       {
           n=in.nextInt();
           int a[] = new int[n];
           int d[] = new int[n];
           
           for(j=0;j<n;j++)
           {
              a[j] = in.nextInt();
           }
           int dd= a[n-1]-a[0];
           for(j=0;j<n-1;j++)
           {
                d[j] = a[j+1]-a[j];
               if(d[j]==1)
               {
                   c++;
               }
                
               
           }
           
           
               if(c==n-1)
               {
                  
                 System.out.println("YES");
               }
               
               else if(dd==1||n==1)
                   {
                      
                       System.out.println("YES");
                       jj++;
                   }
                   
               
              else
              {
                   System.out.println("NO");
                      
               }
           }
       }
        
        
    }
    

