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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner Ent = new Scanner(System.in);
        int casos = Ent.nextInt();
        for (int i = 0; i < casos; i++) {
            int size = Ent.nextInt();
            int arr0[] = new int[size];
            int arr1[] = new int[size];
            for (int j = 0; j < size; j++) {
                int valor = Ent.nextInt();
                arr0[j] = valor;
                arr1[j] = valor;
            }
            Arrays.sort(arr0);
            int menor = 0;
            for (int j = 0; j < arr0.length; j++) {
                if (arr0[0] == arr1[j]) {
                    menor = j;
                    break;
                }
            }
            boolean aux = true;

            for (int j = 0; j < size; j++) {
                if (arr0[j] == arr1[menor]) {
                    menor++;
                    if (menor == size) {
                        menor = 0;
                    }
                } else {
                    aux = false;
                    break;
                }
            }
            if (aux) {
                System.out.println("YES");
            } else {
                for (int j = 0; j < size; j++) {
                    arr0[j] = arr0[j]*-1;
                    arr1[j] = arr1[j]*-1;
                }
                Arrays.sort(arr0);
                menor = 0;
                for (int j = 0; j < arr0.length; j++) {
                    if (arr0[0] == arr1[j]) {
                        menor = j;
                    }
                }
                aux = true;

                for (int j = 0; j < size; j++) {
                    if (arr0[j] == arr1[menor]) {
                        menor++;
                        if (menor == size) {
                            menor = 0;
                        }
                    } else {
                        aux = false;
                        break;
                    }
                }

                if (aux) {
                    System.out.println("YES");
                } else {
                    System.out.println("NO");
                }
            }
        }
    }
}

			    		 		      					 			 			