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
///package Codef;

import java.util.Scanner;

public class A_1203 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int q = s.nextInt();
		outer: for (int i = 0; i < q; i++) {
			int n = s.nextInt();
			int[] a = new int[n];
			for (int j = 0; j < n; j++) {
				a[j] = s.nextInt();

			}
			int l = 0, r = 0;
			int f = a[0];
			int ff = 0;
			if (n > 1) {
				ff = a[1];
				if (ff == f + 1) {
					r = 1;
				} else {
					l = 1;
				}

				for (int j = 2; j < n; j++) {
					if (r == 1) {
						if (a[j] == ff + 1) {
							//System.out.println("HIIIIII");
							ff = a[j];
							continue;
						} else if (a[j] == 1 && a[j - 1] == n) {
							ff = a[j];
							continue;
						} else {
							ff = a[j];
							System.out.println("NO");
							continue outer;
						}
					} else if (l == 1) {
						if (a[j] == ff - 1) {
							ff = a[j];
							continue;
						} else if (a[j] == n && a[j - 1] == 1) {
							ff = a[j];
							continue;
						} else {
							System.out.println("NO");
							ff = a[j];
							continue outer;
						}
					}
					//ff = a[j];
				}
				System.out.println("YES");
			} else {
				System.out.println("YES");
			}

		}
	}

}
