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.ArrayList;
import java.util.Scanner;
import java.util.Vector;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
       // Scanner scanner1 = new Scanner(System.in);
        int q = scanner.nextInt();

        while (q!=0){
            int n = scanner.nextInt();
            ArrayList <Integer> students = new ArrayList<>();
            int min=0;
            for( int i=0;i<n;i++){
                students.add(i,scanner.nextInt());
                if(students.get(i)==1){
                    min = i;
                }
            }
            boolean check = true, check1=true;
            for(int j =1;j<n;j++){
                check &= (students.get((min-j+n)%n) ==j+1);
                check1&= (students.get((min+j+n)%n) ==j+1);
            }
            if( check||check1){
                System.out.println("Yes");
            }
            else {
                System.out.println("No");
            }
            q--;
        }

        /*while (q != 0) {
            boolean check = true;
            int n = scanner.nextInt();
            int students[] = new int[n];
            int min = 0;
            for (int i = 0; i < n; i++) {
                students[i] = scanner.nextInt();
                if (students[i] == 1) {
                    min = i;
                }
            }
            boolean side = true;
            if (min!=0 && min!=n-1) {
                if (students[min + 1] - students[min - 1] > 0) {
                    for (int i = min; i > 0; i--) {
                        if (Math.abs(students[i] - students[i - 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                    for (int i = min + 1; i < n - 2; i++) {
                        if (Math.abs(students[i] - students[i + 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                } else {
                    for (int i = min - 1; i > 0; i--) {
                        if (Math.abs(students[i] - students[i - 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                    for (int i = min; i < n - 2; i++) {
                        if (Math.abs(students[i] - students[i + 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                }
            }else {
                if( min==0){
                    for(int i=1;i<n-1;i++){
                        if (Math.abs(students[i] - students[i + 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                }else {
                    for(int i=n-1;i>0;i--){
                        if (Math.abs(students[i] - students[i - 1]) > 1) {
                            check = false;
                            break;
                        }
                    }
                }
            }
            if (check) {
                System.out.println("Yes");
            } else {
                System.out.println("No");
            }
            q--;
        }*/
    }
}