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 AOddSum {

	public static void main(String[] args) {
		
		Scanner scn = new Scanner(System.in);
		int t = scn.nextInt();
		for(int i=0 ; i<t ; i++) {
			int a = scn.nextInt();
			int arr[] = new int[a];
			for(int j=0 ; j<a ; j++) {
				arr[j] = scn.nextInt();
			}
			if(a==1) System.out.println("YES");
			else if(a==2) {
				int f = Math.abs(arr[0] - arr[1]);
				if(f==1) System.out.println("YES");
				else System.out.println("NO");
			}
			
			else {
				int ar2[] = new int[a-1];
				for(int k=0 ; k<a-1 ; k++) {
					ar2[k] = arr[k] - arr[k+1];
				}
				int c=ar2.length;
				Arrays.sort(arr);
				Arrays.sort(ar2);
				int last = a-1;
				int e = ar2[1];
				
				if(e>0) {
				boolean flag = true;
				for(int s=0 ; s<c-2 ; s++) {
					if(ar2[s+1]!=1) { 
						flag = false;
						break;
					}
				}
				if(flag) {
					int u = Math.abs(ar2[c-1]);
					if(u==a-1 || u==1){
						System.out.println("YES");
					}
					else System.out.println("NO");
				}
				else System.out.println("NO");	
				}
				else {

					boolean flag = true;
					for(int s=0 ; s<c-2 ; s++) {
						if(ar2[s]!=-1) { 
							flag = false;
							break;
						}
					}
					if(flag) {
						if(ar2[c-1]==a-1 || ar2[c-1]==ar2[1]){
							System.out.println("YES");
						}
						else System.out.println("NO");
					}
					else System.out.println("NO");	
					
				}
			}
		}			
	}		
}