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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class test4 {
	public static void main(String[] args) {
		FastReader fr = new FastReader();
		int q = fr.nextInt();
		while(q-- >0){
			int n=fr.nextInt();
			int[] p =new int[n];
			for (int i = 0; i < p.length; i++) {
				p[i] = fr.nextInt();
				p[i]--;
			}
			boolean up = true;
			boolean down = true;
			for(int i =0;i<n-1;i++){
				 up &= (p[i] + 1) % n == p[i + 1];
	             down &= (p[i + 1] + 1) % n == p[i];
	             
			}
			System.out.println((up || down)?"Yes":"No");
			
		}
		
	}
	static class FastReader
	{
		BufferedReader br;
		StringTokenizer st;
 
		public FastReader()
		{
			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());
		}
	}


}