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.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class danceRound {
	static class Scanner {

   		StringTokenizer st;
   		BufferedReader br;
    
   		public Scanner(InputStream system) {
   			br = new BufferedReader(new InputStreamReader(system));
   		}
    
   		public Scanner(String file) throws Exception {
   			br = new BufferedReader(new FileReader(file));
   		}
    
   		public String next() throws IOException {
   			while (st == null || !st.hasMoreTokens())
   				st = new StringTokenizer(br.readLine());
   			return st.nextToken();
   		}
    
   		public String nextLine() throws IOException {
   			return br.readLine();
   		}
    
   		public int nextInt() throws IOException {
   			return Integer.parseInt(next());
   		}
    
   		public double nextDouble() throws IOException {
   			return Double.parseDouble(next());
   		}
    
   		public char nextChar() throws IOException {
   			return next().charAt(0);
   		}
    
   		public Long nextLong() throws IOException {
   			return Long.parseLong(next());
   		}
    
   		public boolean ready() throws IOException {
   			return br.ready();
   		}
    
   		public void waitForInput() throws InterruptedException {
   			Thread.sleep(3000);
   		}
   	}
	
	public static void main(String []args) throws IOException {
 		PrintWriter pw =new PrintWriter(System.out);
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        for(int j=0;j<n;j++) {
        	int m=sc.nextInt();
        	int a[]=new int [m];
        	for(int i=0;i<m;i++)a[i]=sc.nextInt();boolean f=true;
        	if(m!=1) {
        	for(int i=0;i<m-1;i++) {
        		if(a[i]==1||a[i]==n) {
        			if(!(Math.abs(a[i]-a[i+1])==1||Math.abs(a[i]-a[i+1])==m-1)) {f=false;break;}}
        		else{if(!(Math.abs(a[i]-a[i+1])==1)) {f=false;break;}}
        	}}
        	if(f)pw.println("YES");else pw.println("NO");pw.flush();
        }
}}
