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
//package  com.company;
//import java.io.*;
import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner s=new Scanner(System.in);
        int t=s.nextInt();
        while(t-->0){HashMap<Integer,Integer> h=new HashMap<Integer,Integer>();int flag=0;
            int n=s.nextInt();
            int[] a=new int[n];
            //System.out.println(t);
            for(int i=0;i<n;i++){
                a[i]=s.nextInt();}
                for(int i=0;i<n;i++){
                if(i!=0){
                    if(!h.containsKey(a[i]-a[i-1])&&h.size()<=1){
                        //System.out.println(a[i]-a[i-1]+" "+h.size()+" "+a[i]+" "+a[i-1]+" "+i);
                        h.put(a[i]-a[i-1],i);
                    }else if(!h.containsKey(a[i]-a[i-1])&&h.size()>1){
                        System.out.println("NO");flag=1;break;
                    }
                }
            }if(flag==0){int g=0;int f=0;
                for(int i:h.keySet()){
                    if(i!=1&&i!=-1){
                        if(g==1){f=1; System.out.println("NO");break;}
                        else g=1;
                    }
                }
                if(f==0)System.out.println("YES");}
        }
    }
}