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.*;

public class circleOfStudents{

    public static void main(String[] args){

        Scanner s = new Scanner(System.in);

        int inputs = s.nextInt();

        for(int i = 0;i<inputs;i++){

            int arrl = s.nextInt();

            int[] arr = new int[arrl];

            for(int x = 0;x<arrl;x++){
                arr[x] = s.nextInt();
            }


            if(arr[0] > arr[arr.length - 1] || (arr[0] == 1 && arr[arr.length - 1] == arrl)){
                //clockwise check

                boolean bool = true;
                for(int j = 0;j<arrl - 2;j++){
                    if(arr[j] == arrl){
                        if(arr[j+1]!=1){
                            bool = false;
                            break;
                        }
                    }else{
                        if(arr[j]+1 != arr[j+1]){
                            bool = false;
                            break;
                        }
                    }
                }
                if(bool == true){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
            }else if(arr[0] < arr[arr.length - 1] || (arr[0] == arr.length && arr[arr.length - 1] == 1)){
                //anti-clockwise check

                boolean bool = true;
                for(int j = 0;j<=arrl - 2;j++){
                    if(arr[j] == 1){
                        if(arr[j+1]!=arrl){
                            bool = false;
                            break;
                        }
                    }else{
                        if(arr[j] != arr[j+1]+1){
                            bool = false;
                            break;
                        }
                    }
                }
                if(bool == true){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }

            }else{
                System.out.println("YES");
            }

        }
    }
}