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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
		int t;
		t=in.nextInt();
		for(int i=0;i<t;i++)
			solver.solve(1, in, out);
        out.close();
    }
	
	

    static class Task {
		
		public boolean inc(int[] a,int n){
			int cnt,ind;
			ind=n;
			cnt=0;
			for(int i=1;i<n;i++){
				if(a[i] == a[i-1]+1)
					continue;
				else{
					cnt++;
					ind=i;
					break;
				}		
			}
			for(int i=ind+1;i<n;i++){
				if(a[i] == a[i-1]+1)
					continue;
				else{
					return false;
				}	
			}
			
			return true;
			
		}
		public boolean dec(int[] a,int n){
			int cnt,ind;
			cnt=0;
			ind=n;
			for(int i=1;i<n;i++){
				if(a[i]+1==  a[i-1])
					continue;
				else{
					cnt++;
					ind=i;
					break;
				}		
			}
			for(int i=ind+1;i<n;i++){
				if(a[i]+1 ==  a[i-1])
					continue;
				else{
					return false;
				}	
			}
			
			return true;
			
		}
		
		public int solve(int testNumber, InputReader in, PrintWriter out) {
			int n;
			int[] a;
			String s;
			s="NO";
			n=in.nextInt();
			a=new int[n];
			for(int i=0;i<n;i++)
				a[i]=in.nextInt();
			if(inc(a,n) || dec(a,n))
				s="YES";
			out.println(s);
			return 0;
		}
	}
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}