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.*;

public class Dance {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t > 0) {
            int n = sc.nextInt();
            int[] arr =new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] =sc.nextInt();
            }
            if(n==1 ){
                if(arr[0]==1){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
            }else{
                int first= arr[0];
                boolean clockwise = true, anti=true;
                for (int i = 1; i < n; i++) {
                    if(arr[i]==first+1){
                        first++;
                    }else{
                        if(first==n && arr[i]==1){
                            first = 1;
                        }else{
                            clockwise = false;
                            break;
                        }
                    }
                }
                first = arr[0];
                for (int i = 1; i < n; i++) {
                    if(arr[i]==first-1){
                        first--;
                    }else{
                        if(first==1 && arr[i]==n){
                            first = n;
                        }else{
                            anti = false;
                            break;
                        }
                    }
                }
                boolean ans = clockwise || anti;
                if(ans){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
            }
            t--;
        }
    }


    //Fast Reader Class
    static class FastReader {
        BufferedReader reader;
        StringTokenizer mStringTokenizer;

        public FastReader() {
            reader = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (mStringTokenizer == null || !mStringTokenizer.hasMoreElements()) {
                try {
                    mStringTokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return mStringTokenizer.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 = reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
