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.InputStreamReader;
import java.io.IOException;

/*
https://codeforces.com/contest/1203/problem/A
*/

public class CIrcleOfStudents {

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		// number of queries
		int q = Integer.parseInt(br.readLine());

		while (q-- > 0) {
			int n = Integer.parseInt(br.readLine());

			// array to store number of students
			int arr[] = new int[n];
			// to which direction it will go
			char direction = 'N';
			int current = 0;
			int previous = 0;

			// round dance is possible or not
			boolean flag = true;

			String[] str = br.readLine().split(" ");

			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(str[i]);

				if (i == 1) {
					current = arr[1];
					previous = arr[0];
					if ((current == previous - 1) || (previous == 1 && current == n)) {
						direction = 'L';
					} else if ((current == previous + 1) || (previous == n && current == 1)) {
						direction = 'R';
					}
				} else if (i > 1) {
					previous = arr[i - 1];
					current = arr[i];
					/*
					 * System.out.println("1--i = " + i + ", n=" + n + ", direcion = " + direction +
					 * " , current = " + current + ", previious = " + previous + ", flag = " +
					 * flag);
					 */
					if (direction == 'L') {
						if (previous == 1 && current != n && flag == true) {
							flag = false;
						} else if (previous != 1 && current != previous - 1 && flag == true) {
							flag = false;
						}
					} else if (direction == 'R' && flag == true) {
						if (previous == n && current != 1 && flag == true) {
							flag = false;
						} else if (previous != n && current != previous + 1 && flag == true) {
							flag = false;
						}

					}
				}
				/*
				 * System.out.println("2--i = " + i + ", direcion = " + direction +
				 * " , current = " + current + ", previious = " + previous + ", flag = " +
				 * flag);
				 */
			}
			if (flag == false || (direction == 'N' && n > 1))
				System.out.println("NO");
			else
				System.out.println("YES");
		}
	}
}
