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.util.*;
import java.io.*;
public class a {
	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		
		int T = sc.nextInt();
		while (T-- > 0) {
			int n = sc.nextInt();
			int[] arr = new int[n*2];
			
			if (n == 1) {
				System.out.println("YES");
				continue;
			}
			
			for (int i = 0 ; i < n ; i++) {
				arr[i] = sc.nextInt();
				arr[i+n] = arr[i];
			}
			
			int s = 1;
			int max = 0;
			for (int i = 0 ; i < n*2 - 1 ; i++) {
				if (arr[i] > arr[i+1]) {
					s++;
				} else {
					s=1;
				}
				max = Math.max(max, s);
			}
			s = 1;
			for (int i = 0 ; i < n*2 - 1 ; i++) {
				if (arr[i] < arr[i+1]) {
					s++;
				} else {
					s = 1;
				}
				max = Math.max(max, s);
			}
			
			if (max == n) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
			
		}
		
		
		
		
		
	}

	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    public long nextLong() throws IOException {
	        return Long.parseLong(next());
	    }
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	}
}
