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 circle {
	public void run() throws Exception {
		Scanner file = new Scanner(System.in);
		int times = file.nextInt();
		for (int i = 0; i < times; i++) {
			int n = file.nextInt();
			ArrayList<Integer> x=  new ArrayList();
			for (int j = 0; j < n; j++) x.add(file.nextInt());
			int ind = x.indexOf(1);
			ArrayList<Integer> z = new ArrayList(), a = new ArrayList();
			for (int j = ind; j >= 0; j--) z.add(x.get(j));
			for (int j = x.size() - 1; j > ind; j--) z.add(x.get(j));
			for (int j = ind; j < x.size(); j++) a.add(x.get(j));
			for (int j = 0; j < ind; j++) {
				a.add(x.get(j));
			}
			int cur = 1, cur2 = n;
			boolean aa = true, bb = true;
			for (int ii= 0; ii < z.size(); ii++) {
				if (z.get(ii) != cur && a.get(ii) != cur) {
					aa = false;
					break;
				}
				cur++;
			}
			for (int ii = 0; ii < a.size(); ii++) {
				if (a.get(ii) != cur2 && z.get(ii) != cur2) {
					bb = false;
					break;
				}
				cur2++;
			}
			//System.out.println(z);
			//System.out.println(a);
			System.out.println(aa || bb ? "YES" : "NO");
		}
	}

	public static void main(String[] args) throws Exception {
		new circle().run();
	}

}