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.*;
import java.io.*;

public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		FastReader sc=new FastReader();
	   int T= sc.nextInt();
	   while(T-->0)
	   
	   {
	       int n= sc.nextInt();
	       int a[]=new int[n];
	       int f=0;
	       int j=0;
	       for(int i=0;i<n;i++)
	       {a[i]=sc.nextInt();
	       if(a[i]==1)
	       j=i;}
	       if(n==1)
	       System.out.println("YES");
	       else
	       {
	       if(j==n-1)
	       {
	           if(a[0]==2)
	           f=1;
	           else if(a[0]==n)
	           f=2;
	           else
	           f=3;
	       }
	       else
	       {
	           if(a[j+1]==2)
	           f=1;
	           else if(a[j+1]==n)
	           f=2;
	           else
	           f=3;
	       }
	       if(f==1)
	       {
	           for(int i=1;i<n;i++)
	           {
	               if(j!=n-1 && i!=j+1 && a[i]!=a[i-1]+1)
	               {
	                   f=3;
	                   break;
	               }
	           }
	       }
	       else if(f==2)
	       {
	           for(int i=1;i<n;i++)
	           {
	               if(j!=n-1 && i!=j+1 && a[i]+1!=a[i-1])
	               {
	                   f=3;
	                   break;
	               }
	           }
	       }
	       if(f==2 || f==1)
	       System.out.println("YES");
	       else
	       System.out.println("NO");
	       }
	   }
	 }
	 
	 public static char func(long l,long l1)
	 {
	     char x1='a';
	      if(l%2==0)
	            {
	                if(l1<=l/2)
	                x1='L';
	                else
	                x1='R';
	            }
	            else
	            {
	                if(l1<(l+1)/2)
	                {
	                    x1='L';
	                }
	                else if(l1==(l+1)/2)
	                x1='B';
	                else
	                x1='R';
	            }
	            return x1;
	 }
	  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 int gcd(int a,int b)
		{
		    if(a%b==0)
		    return b;
		    return gcd(b,a%b);
		}
		
	static ArrayList<Integer> sieve(int n) 
    { 
        ArrayList<Integer> arr=new ArrayList<Integer>();
        boolean prime[] = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
          
        for(int i = 2; i <= n; i++) 
        { 
            if(prime[i] == true) 
                arr.add(i); 
        } 
        return arr;
    } 
      
	static float power(float x, int y) 
    { 
        float temp; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2);  
          
        if (y%2 == 0) 
            return temp*temp; 
        else
        { 
            if(y > 0) 
                return x * temp * temp; 
            else
                return (temp * temp) / x; 
        } 
    } 
    static long pow(int a,int b)
    {
        long result=1;
        if(b==0)
        return 1;
        long x=a;
        while(b>0)
        {
            if(b%2!=0)
            result*=x;
            
            x=x*x;
            b=b/2;
        }
        return result;
    }
}