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 Main{
        public static void main(String [] args){
                Scanner sc=new Scanner(System.in);
                int t=sc.nextInt();
                while(t-->0){
                        int n=sc.nextInt();
                        int a[]=new int[n];
                        int x=0;
                        for(int i=0;i<n;i++){
                                a[i]=sc.nextInt();
                                if(a[i]==1)
                                x=i;
                        }
                        if(n<=2){
                        System.out.println("YES");
                        }
                        else{
                                boolean p=true;
                                if(a[0]==1){
                                    if(a[1]==n){
                                    int t2=n;
                                    for(int i=1;i<n;i++){
                                        if(a[i]!=t2){
                                      
                                            p=false;
                                            break;
                                        }
                                        t2--;
                                    }
                                    }
                                    else if(a[1]==2){
                                        for(int i=1;i<n;i++){
                                            if(a[i]!=i+1){
                                                p=false;
                                                break;
                                            }
                                        }
                                    }
                                }
                                else if(a[1]<a[0]){
                                        
                                   for(int i=0;i<x;i++){
                                           if(a[i]!=x+1-i){
                                                   p=false;
                                                   break;
                                           }
                                   }
                                   int t1=n;
                                   for(int i=x+1;i<n;i++){
                                           if(a[i]!=t1){
                                                   p=false;
                                                   break;
                                                   
                                           }
                                           t1--;
                                   }
                                }
                                else{
                                        int k=1;
                                        for(int j=x;j<n;j++){
                                                if(a[j]!=k)
                                                {
                                                        p=false;
                                                        break;
                                                }
                                                k++;
                                        }
                                        for(int j=0;j<x;j++){
                                                if(a[j]!=a[n-1]+j+1){
                                                        p=false;
                                                        break;
                                                        
                                                }
                                        }
                                }
                                if(p){
                                        System.out.println("YES");
                                        
                                }
                                else{
                                     System.out.println("NO");   
                                }
                        }
                }
        }
}

