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 Circle2{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int q = sc.nextInt();
		for(int i=0;i<q;i++){
			int n = sc.nextInt();
			int arr[] = new int[n];
			int min = Integer.MAX_VALUE, max = Integer.MIN_VALUE, min_i = 0, max_i=0;
			for(int j=0; j<n; j++){
				arr[j] = sc.nextInt();
				if(arr[j] > max){
					max = arr[j];
					max_i = j;
				}
				if(arr[j] < min){
					min = arr[j];
					min_i = j;
				}
			}
			if(n==1){
				System.out.println("YES");
				continue;
			}
			//System.out.println(min_i + " " + max_i);
			int flag = 0;
			if(arr[min_i]+1== arr[(min_i+1)%n]){
				flag = 1;
			}
			else if(arr[max_i]-1== arr[(max_i+1)%n]){
				flag = 0;
			}
			else{
				System.out.println("NO");
				continue;
			}
			//System.out.println(flag);
			
			
			int temp = 0;
			if(flag==1){
				for(int k = min_i;;){
					//System.out.println(arr[k]+" "+arr[(k+1)%n]);
					if(arr[k%n]+1!=arr[(k+1)%n]){
						temp = 1;
						break;
					}
					k = (k+1)%n;
					if(k%n==max_i){
						break;
					}
				}
			}
			else{
				for(int k = max_i;;){
					if(arr[k%n]-1!=arr[(k+1)%n]){
						temp = 1;
						break;
					}
					k = (k+1)%n;
					if(k%n==min_i){
						break;
					}
				}
			}
			if(temp==1){
				System.out.println("NO");
			} else{
				System.out.println("YES");
			}
		}
	}
}