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 dance {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while(t-->0) {
			int n = s.nextInt();
			int[] arr = new int[n];
			for(int i = 0; i < n; i++) {
				arr[i]=s.nextInt();
			}
			if(n==1) {
				System.out.println("YES");
				continue;
			}
			int min = Integer.MAX_VALUE;
			int mini = -1;
			for(int i = 0; i < n; i++) {
				if(arr[i]<min) {
					mini = i;
					min = arr[i];
				}
			}
			int temp = mini;
			int next = mini + 1;
			int prev = mini - 1;
			if(next>=n) {
				next-=n;
			}
			int flag = -1;
			if(prev<0) {
				prev+=n;
			}
			if(arr[next]==n) {
				flag = 1;
			}
			if(arr[next]==arr[mini]+1) {
				flag = 0;
			}
			if(flag==-1) {
				System.out.println("NO");
				continue;
			}
			for(int i = 0; i < n-1; i++) {
				if(flag==0) {
					if(mini>=n) {
						mini-=n;
					}
					next = mini+1;
					if(next>=n) {
						next-=n;
					}
					if(arr[next]!=arr[mini]+1) {
						System.out.println("NO");
						flag = -1;
						break;
					}
					mini++;
				}else if(flag==1) {
					if(mini<0) {
						mini+=n;
					}
					prev = mini-1;
					if(prev<0) {
						prev+=n;
					}
					if(arr[prev]!=arr[mini]+1) {
						System.out.println("NO");
						flag = -1;
						break;
					}
					mini--;
				}
			}
			if(flag!=-1) {
				System.out.println("YES");
			}
		}
	}

}
