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.lang.*;
public class MyClass 
{
    public static void main(String args[])throws Exception
    {int i,j,n,l,min,max,c,index,f;
      Scanner s = new Scanner(System.in);
        n = s.nextInt();
        for(i = 0; i < n; i++)
        {f=0;
        min=200;
        max=0;
        c=0;
        index=0;
        
            l=s.nextInt();
            if(l<2)
            {
                System.out.println("YES");
                continue;
            }
            else
            {int a[]=new int[l]; 
            int arr[]=new int[l];
                
             for(j=0;j<l;j++)
            {
                a[j] = s.nextInt();
                if(a[j]>max)
                {
                    max=a[j];
                    index=j;
                }
                if(a[j]<min)
                {
                    min=a[j];
                }
            }
          for(j=index;c<l;j++,c++)
          {
              arr[c]=a[j];
              if(j==(l-1))
                  j=-1;
          }
          if( (Math.abs(arr[0]-arr[1])!=1) && (arr[1])==min)
           {
              for(j=1;j<l-1;j++)
                {
              if((arr[j+1]-arr[j])!=1)
              {
                  f=1;
                  break;
              }
                }
           }
       else
         {
             for(j=0;j<l-1;j++)
          {
              if((arr[j]-arr[j+1])!=1)
              {
                  f=1;
                  break;
              }
          }
         }
          if(f==1)
           System.out.println("NO");
           else
           System.out.println("YES");
        }
        }
    }
}