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 Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);

        int t = s.nextInt();
        while(t-->0){
            int n = s.nextInt();
            ArrayList<Integer> a = new ArrayList<>();

            for(int i = 0 ; i < n ; i++){
                a.add(s.nextInt());
            }
            if( n == 1 || n == 2 ){
            System.out.println("YES");
            continue;}

            int ind = a.indexOf(1);
            int x = a.indexOf(2);
            int y = 0;
            if(x - ind > 0 && x != n-1)
            y = 1;
            else if(ind == n-1)
            y = 1;
            else
            y = -1;

            //System.out.println(y);
            int flag = 1;

            if(y==1){
                for(int i = 0 ; i < n ; i++){
                    int in = (ind+i)%n;
                    if(a.get(in) != i+1){
                        flag = 0 ;
                        break;
                    }
                }
            }else{
                for(int i = 0 ; i < n ; i++){
                    int in = (ind-i+n)%n;
                    if(a.get(in) != i+1){
                        flag = 0 ;
                        break;
                    }
                }
            }
            if(flag ==1)
            System.out.println("YES");
            else
            System.out.println("NO");
            
        }
        //System.out.println("Hello World!");
    }
}