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 Codeforces1 {

   
    public static void main(String[] args) {
     
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int i=0;i<t;i++){
            int n=sc.nextInt();
            int a[]=new int[n];
            boolean flag=true;
            for(int j=0;j<n;j++){
                a[j]=sc.nextInt();
            }
            if((n==1)||(n==2)||(n==3)){
                
            }
            else{
                if(a[0]==1){
                    if(a[1]==2){
                        for(int j=2;j<n;j++){
                            if(a[j]==(j+1)){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                    }
                    else if(a[n-1]==2){
                        for(int j=1;j<n-1;j++){
                            if(a[j]==n-j+1){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                    }
                    else{
                        flag=false;
                    }
                }
                else if(a[n-1]==1){
                    if(a[n-2]==2){
                        for(int j=0;j<n-3;j++){
                            if(a[j]==n-j){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                    }
                    else if(a[0]==2){
                        for(int j=0;j<n-1;j++){
                            if(a[j]==j+2){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                    }
                    else{
                        flag=false;
                    }
                }
                else{
                    int ind=-1;
                    for(int j=1;j<n;j++){
                        if(a[j]==1){
                            ind=j;
                            break;
                        }
                    }
                    if(a[ind+1]==2){
                        int h=ind-1;
                        int p=a[0];
                        for(int j=ind+2;j<n;j++){
                            if(a[j]==(j-h)){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                        for(int j=1;j<ind;j++){
                            if(a[j]==j+p){
                            }
                            else{
                                 flag=false;
                                 break;
                            }
                        }
                    }
                    else if(a[ind-1]==2){
                        int z=ind+1+a[ind+1];
                        int x=a[0];
                        for(int j=0;j<ind;j++){
                            if(a[j]==x-j){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                        for(int j=ind+1;j<n;j++){
                            if(a[j]==z-j){
                            }
                            else{
                                flag=false;
                                break;
                            }
                        }
                    }
                    else{
                       
                    }
                }
            }
            if(flag==false){
                System.out.println("NO");
            }
            else{
                System.out.println("YES");
            }
            
        }
    }
    
}
