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 A {

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

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

        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());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }

    }

    static InputReader r = new InputReader(System.in);
    static PrintWriter pw = new PrintWriter(System.out);

    /** CHECKLIST:
     * LIMITS (DOES BRUTE FORCE WORK?)
     * CHECK ALL PARAMETERS
     * INT VS LONG
     */
    public static void main(String[] args) {
        
        int q = r.nextInt();
        for(int query = 1; query <= q; query++){
            int n = r.nextInt(); // num students
            StringBuilder sb = new StringBuilder();
            for(int i = 1; i <= n; i++){
                sb.append(r.nextInt());
            }
            String s = sb.toString();
            s += s;
            StringBuilder key1 = new StringBuilder();
            StringBuilder key2 = new StringBuilder();
            for(int i = 1; i <= n; i++){
                key1.append(i);
            }
            for(int i = n; i >= 1; i--){
                key2.append(i);
            }
            String s1 = key1.toString();
            String s2 = key2.toString();
            if(s.contains(s1) || s.contains(s2)){
                pw.println("YES");
            } else{
                pw.println("NO");
            }
        }

        pw.close();
    }
}

/**
                _        _                 _                                                
               | |      | |               | |                                               
   ___ ___   __| | ___  | |__  _   _    __| | __ _ _ __ _ __ ___ _ __     _   _  __ _  ___  
  / __/ _ \ / _` |/ _ \ | '_ \| | | |  / _` |/ _` | '__| '__/ _ \ '_ \   | | | |/ _` |/ _ \ 
 | (_| (_) | (_| |  __/ | |_) | |_| | | (_| | (_| | |  | | |  __/ | | |  | |_| | (_| | (_) |
  \___\___/ \__,_|\___| |_.__/ \__, |  \__,_|\__,_|_|  |_|  \___|_| |_|   \__, |\__,_|\___/ 
                                __/ |                               ______ __/ |            
                               |___/                               |______|___/             
 */