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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedHashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;


 public class hello2
 {static class FastReader 
       { 
           BufferedReader br; 
           StringTokenizer st; 
     
           public FastReader() 
           { 
               br = new BufferedReader(new
                        InputStreamReader(System.in)); 
           } 
     
           String next() 
           { 
               while (st == null || !st.hasMoreElements()) 
               { 
                   try
                   { 
                       st = new StringTokenizer(br.readLine()); 
                   } 
                   catch (IOException  e) 
                   { 
                       e.printStackTrace(); 
                   } 
               } 
               return st.nextToken(); 
           } 
     
           int nextInt() 
           { 
               return Integer.parseInt(next()); 
           } 
     
           long nextLong() 
           { 
               return Long.parseLong(next()); 
           } 
     
           double nextDouble() 
           { 
               return Double.parseDouble(next()); 
           } 
     
           String nextLine() 
           { 
               String str = ""; 
               try
               { 
                   str = br.readLine(); 
               } 
               catch (IOException e) 
               { 
                   e.printStackTrace(); 
               } 
               return str; 
           } 
         
       }
    
    static String sum (String s)
    {
        String s1 = ""; 
        
        if(s.contains("a"))
            s1+="a";
        if(s.contains("e"))
            s1+="e";
        if(s.contains("i"))
            s1+="i";
        if(s.contains("o"))
            s1+="o";
        if(s.contains("u"))
            s1+="u";
        
            return s1;
            
        
    }
    

    public static HashMap<String, Integer> sortByValue(HashMap<String, Integer> hm) 
    { 
        // Create a list from elements of HashMap 
        List<Map.Entry<String, Integer> > list = 
               new LinkedList<Map.Entry<String, Integer> >(hm.entrySet()); 
  
        // Sort the list 
        Collections.sort(list, new Comparator<Map.Entry<String, Integer> >() { 
            public int compare(Map.Entry<String, Integer> o1,  
                               Map.Entry<String, Integer> o2) 
            { 
                return (o1.getValue()).compareTo(o2.getValue()); 
            } 
        }); 
          
        // put data from sorted list to hashmap  
        HashMap<String, Integer> temp = new LinkedHashMap<String, Integer>(); 
        for (Map.Entry<String, Integer> aa : list) { 
            temp.put(aa.getKey(), aa.getValue()); 
        } 
        return temp; 
    } 
    
    
public static void main(String args[])
    {
        FastReader input =new FastReader();
        
        int q = input.nextInt();
        
        
        while(q-->0)
        {
        	int n = input.nextInt();
        	int a[] = new int[n];
        	int min = 100000;
        	int x =0;
        	for(int i=0;i<n;i++)
        	{
        		a[i] = input.nextInt();
        	}
        	
        	int count =0;
        	for(int i=1;i<n;i++)
        	{
        		if(Math.abs(a[i]-a[i-1])==1 || Math.abs(a[i]-a[i-1])==n-1)
        		{
        			count++;
        		}
        	}
        	
        	if(count!=n-1)
        	{
        		System.out.println("NO");
        	}
        	else
        	{
        		System.out.println("YES");
        	}
        	
        	
        	
        }
        
    }	
    static boolean isPrime(int n) 
    { 
        // Corner case 
        if (n <= 1) 
            return false; 
  
        // Check from 2 to n-1 
        for (int i = 2; i < n; i++) 
            if (n % i == 0) 
                return false; 
  
        return true; 
    } 
 }
 
 
 class Pair
 {
     int a;
     int b;
     Pair(int a,int b)
     {
         this.a=a;
         this.b=b;
     }
 }
  