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.Scanner;

public class CircleOfStudents {

    static String solution(int[] arr){
        int maxIndex=0, max=-1, minIndex=0, min=201;
        int n = arr.length;
        for(int i=0; i<n; i++){
            if(arr[i] > max){
                max = arr[i];
                maxIndex=i;
            }
            if(arr[i]<min){
                min = arr[i];
                minIndex = i;
            }
        }


        //For Ascending order.
        int i = minIndex+1;
        int prev = arr[minIndex];

        while(true){
            if(arr[i%n] == min) {

                return "YES";
            }
            if(arr[i%n] - prev == 1){
                break;
            }
            prev=arr[i%n];
            i++;
        }

        i = maxIndex+1;
        prev = arr[maxIndex];
        while(true){
            if(arr[i%n] == max) {
                return "YES";
            }
            if(arr[i%n] -  prev == -1){
                break;
            }
            prev = arr[i%n];
            i++;
        }
        return "NO";
    }

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        int t = in.nextInt();

        while (t-- != 0) {
            int n = in.nextInt();
            int[] arr = new int[n];
            for (int z = 0; z < n; z++) {
                arr[z] = in.nextInt();
            }
            System.out.println(solution(arr));
        }
    }

}
