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.util.*;
 
public class Main
{
    static boolean compareOrder(int[] a, int[] b)
    {
        b = a.clone();
        Arrays.sort(b);
        
        for(int i=0; i<a.length; i++)
        {
            int count = 0, k = 0;
            for(int j=b.length-i; j<b.length; j++,k++)
                if(a[k] == b[j]) count++;
            for(int j=0; j<b.length-i; j++,k++)
                if(a[k] == b[j]) count++;
            if(count == a.length) return true;
        }
        for(int i=0; i<a.length; i++)
        {
            int count = 0, k = 0;
            for(int j=b.length-i-1; j>=0; j--,k++)
                if(a[k] == b[j]) count++;;
            for(int j=b.length-1; j>=b.length-i; j--, k++)
                if(a[k] == b[j]) count++;
            if(count == a.length) return true;
        }
        return false;
    }
      
    public static void main(String[] args) throws IOException 
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
	      
            int n = Integer.parseInt(st.nextToken());
            for(int i=0; i<n; i++)
            {
                st = new StringTokenizer(br.readLine());
                int t = Integer.parseInt(st.nextToken()); 
                int[] a = new int[t], b = new int[t];
                
                st = new StringTokenizer(br.readLine());
                for(int j=0; j<t; j++)
                    a[j] = Integer.parseInt(st.nextToken());
                
                System.out.println(compareOrder(a,b) == true? "YES": "NO");
            }

	}
}
