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.*;
import java.util.*;

public class Main {
	
	static class Scanner
	{
	    BufferedReader buf;
	    StringTokenizer tok;
	    Scanner()
	    {
	        buf = new BufferedReader(new InputStreamReader(System.in));
	    }
	    
	    boolean hasNext()
	    {
	        while(tok == null || !tok.hasMoreElements()) 
	        {
	            try
	            {
	                tok = new StringTokenizer(buf.readLine());
	            } 
	            catch(Exception e) 
	            {
	                return false;
	            }
	        }
	        return true;
	    }
	    
	    String next()
	    {
	        if(hasNext()) return tok.nextToken();
	        return null;
	    }
	    
	    int nextInt()
	    {
	        return Integer.parseInt(next());
	    }
	    
	    long nextLong()
	    {
	        return Long.parseLong(next());
	    }
	    
	    double nextDouble()
	    {
	        return Double.parseDouble(next());
	    }
	    
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int q = sc.nextInt();
		while(q-- > 0) {
			int n = sc.nextInt();
			boolean counter = false, flag = false;
			int pre = sc.nextInt();
			for(int i = 1; i < n; i++) {
				int cur = sc.nextInt();
				int num = cur - pre;
				pre = cur;
				if(i == 1) {
					if(num == -1 || num == n-1) counter = true;
					else if(num == 1 || num == 1-n) counter = false;
					else flag = true;
				}
				else {
					if(counter && (num != -1 && num != n-1))flag = true;
					if(!counter && (num != 1 && num != 1-n)) flag = true;
				}
			}
			if(flag) out.println("NO");
			else out.println("YES");
		}
		out.close();
	}
	
	
    
   
}