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
/*
 * Remember a 6.89 student can know more than a 10.0 student.
 * Grades don't determine intelligence, they test obedience. 
 * I Never Give Up.
 * I will become Candidate Master today.
 * I will defeat Saurabh Anand.
 * Skills are Cheap,Passion is Priceless.
 */
import java.util.*;
import java.util.Map.Entry;
import java.io.*;
 
import static java.lang.System.out;
import static java.util.Arrays.*;
import static java.lang.Math.*;
 
public class ContestMain{
	private static Reader in=new Reader();
	private static StringBuilder ans=new StringBuilder();
	private static long MOD=(long)1e9+7;
	private static final int N=(int) (1e5+7); // 1e5+7
    private static final double EPS=1e-9;
    private static final int LIM=26;
    private static final double PI=3.1415;
//    private static ArrayList<Integer> v[]=new ArrayList[N];
//    private static int color[]=new int[N];
//	private static boolean mark[]=new boolean[N];
//    private static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//    private static ArrayList<Pair> v[]=new ArrayList[N];
	private static long powmod(long x,long n){
		if(n==0||x==0)
			return 1;
		else if(n%2==0)
			return(powmod((x*x)%MOD,n/2));
		else
			return (x*(powmod((x*x)%MOD,(n-1)/2)))%MOD;
	}
	private static void shuffle(long[] arr){
		for(int i=arr.length-1;i>=2;i--){
			int x=new Random().nextInt(i-1);
			long temp=arr[x];
			arr[x]=arr[i];
			arr[i]=temp;
		}
	}
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
//    private static boolean check(int x,int y){
//        if((x>=0&&x<n)&&(y>=0&&y<m)&&mat[x][y]!='X'&&!visited[x][y])return true;
//        return false;
//    }
    
	public static void main(String[] args) throws IOException{
		int q=in.nextInt();
		int n,ar[],c;
		boolean f1,f2;
		while(q-->0){
			n=in.nextInt();
			ar=new int[n];
			for(int i=0;i<n;i++)
				ar[i]=in.nextInt();
			f1=true;
			c=ar[0];
			for(int i=1;i<n;i++){
				c=(c+1)%(n+1);
				if(c==0)c=1;
				if(ar[i]!=c){f1=false;break;}
			}
			c=ar[0];
			f2=true;
			for(int i=1;i<n;i++){
				c=(c-1)%(n+1);
				if(c<=0)c+=n;
				if(ar[i]!=c){f2=false;break;}
			}
			if(f1||f2)ans.append("YES\n");
			else ans.append("NO\n");
		}
		out.print(ans);
	}
	static class Pair<T> implements Comparable<Pair>{
		int l;
		int r;
		Pair(){
			l=0;
			r=0;
		}
		Pair(int k,int v){
			l=k;
			r=v;
		}
		@Override
		public int compareTo(Pair o){
			if(o.r!=r)
				return (int)-(r-o.r);
			else
				return (int)-(l-o.l);
		}
		// Fenwick tree question comparator
//        @Override
//        public int compareTo(Pair o) {
//            if(o.r!=r)return (int) (r-o.r);
//            else return (int)(l-o.l);
//        }
	}
 
	static class Reader{
		BufferedReader br;
		StringTokenizer st;
 
		public Reader(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{
 
					st=new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt(){
			return Integer.parseInt(next());
		}
 
		long nextLong(){
			return Long.parseLong(next());
		}
 
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String nextLine(){
			String str="";
			try{
				str=br.readLine();
			}catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
//		char nextChar(){
//			return next().charAt(0);
//		}
	}
}