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 A1203 {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        int n;
        int arr[];
        int diff,ndiff;
        boolean no = false;
        while (t-- != 0) {
            no = false;
            n = input.nextInt();
            arr = new int[n];
            diff = -2;
            for(int i=0;i<n;i++){
                arr[i] = input.nextInt();
            }
            if(n == 1){
                if(Math.abs(arr[0]) == 1)
                    System.out.println("YES");
                else
                    System.out.println("NO");
            }
            else{
                for(int i=1;i<n;i++){
                    if(arr[i] == n && arr[i-1] == 1){
                        if(diff == -2)
                            diff = 1;
                        else if(diff != 1){
                            no = true;
                            break;
                        }
                    }else if(arr[i] == 1 && arr[i-1] == n){
                        if(diff == -2)
                            diff = -1;
                        else if(diff != -1){
                            no = true;
                            break;
                        }
                    }else{
                        if(diff == -2){
                            diff = arr[i-1] - arr[i];
                            if(Math.abs(diff)!=1){
                                no = true;
                                break;
                            }
                            continue;
                        }else{
                            ndiff = arr[i-1] - arr[i];
                            if(ndiff != diff){
                                no = true;
                                break;
                            }
                        }
                    }
                }
                if(no){
                    System.out.println("NO");
                }else{
                    System.out.println("YES");
                }
            }
        }
        input.close();
    }
}