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.nio.Buffer;

import java.util.*;
public class ACM {

    public static void main(String[] args) throws IOException {

        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        int q=Integer.parseInt(bf.readLine());
        while(q-->0){
        int z=Integer.parseInt(bf.readLine());
        String st=bf.readLine();
        String a[]=st.split(" ");
         boolean b=false;
        int x=st.indexOf("1")/2;
        if(z==1){System.out.println("YES");}
        else{
            
        if(x==0){int temp=Integer.parseInt(a[x])-Integer.parseInt(a[x+1]);
           // System.out.println("temp:"+temp);
          if(temp!=-1&&temp!=-z+1){System.out.println("NO");}
          else if(temp==-1){
        
         for(int i=0;i<z-1;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=-1){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
          }
            else if(temp==-z+1){
            
         for(int i=1;i<z-1;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=(1)){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
            }
           
        }else if(x==z-1){
        ////
int temp=Integer.parseInt(a[x])-Integer.parseInt(a[x-1]);
          
          if(temp!=-1&&temp!=-z+1){System.out.println("NO");}
          else if(temp==-1){
        
         for(int i=0;i<z-2;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=1){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
          }
            else if(temp==-z+1){
            
         for(int i=0;i<z-2;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=(-1)){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
            }
                   

////
        }
        else {
        ////
int temp=Integer.parseInt(a[x])-Integer.parseInt(a[x-1]);
          int temp1=Integer.parseInt(a[x])-Integer.parseInt(a[x+1]);
           
          if((temp==-1&&temp1==-z+1)||(temp1==-1&&temp==-z+1)){
           if(temp==-1){
        
         for(int i=x;i>0;i--){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i-1]))!=-1){System.out.println("NO");b=true;break;}
         
         }
         for(int i=x+1;i<z-1;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=1){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
          }
            else if(temp==-z+1){
       for(int i=x-1;i>0;i--){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i-1]))!=1){System.out.println("NO");b=true;break;}
         
         }
         for(int i=x+1;i<z-1;i++){
         if((Integer.parseInt(a[i])-Integer.parseInt(a[i+1]))!=-1){System.out.println("NO");b=true;break;}
         
         }
         if(!b){System.out.println("YES");}
            }
                   

////
        }else{System.out.println("NO");}}
        }
        }
         
       
   
  
    
    }
}
