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.*;
import java.io.*;

public class CircleOfStudents{

	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int test = Integer.parseInt(br.readLine());
		
		while(test-- > 0){
			int n = Integer.parseInt(br.readLine());
			
			String s[] = br.readLine().trim().split(" ");
			int a[] = new int[n];
			
			int o=-1;
			for(int i=0;i<n;i++){
				a[i] = Integer.parseInt(s[i]);
				if(a[i]==1){
					o=i;
				}
			}
			
			
			boolean sorted =true;
			
			for(int i=1;i<n;i++){
				if(a[i-1]>a[i]){
					sorted = false;
					break;
				}
			}
			
			
			if(o==0 && sorted){
				System.out.println("YES");
				continue;
			}else{
			
			for(int i=0;i<=o/2;i++){
				
				int t = a[i];
				a[i] = a[o-i];
				a[o-i] = t;
				
			}
			
			for(int i=o+1;i<=(n+o)/2;i++){
				int t = a[i];
				a[i] = a[n-i+o];
				a[n-i+o] = t;	
			}			
			}
			
			/*for(int i=0;i<n;i++){
				System.out.print(a[i]+" ");
			}*/
			
			boolean c = true;
			if(a[0]>a[1]){
				
				int i=0;
				while(i<n-1){
					if(a[i]<a[i+1]){
						c=false;	
					}
					i++;
				}
				
			}else{
				int i=0;
				while(i<n-1){
					if(a[i]>a[i+1]){
						c=false;	
					}
					i++;
				}
			}
			
			if(c){
				System.out.println("YES");
			}else{
				System.out.println("NO");
			}
		}
	}
}


