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.Scanner;

public class Students {

	public static void main(String[] args) {
		Scanner s = new Scanner (System.in);
		
		int q = s.nextInt();
		for (int i = 0; i < q; i++) {
			int[] n = new int[s.nextInt()];
			
			for (int j = 0; j < n.length; j++) {
				n[j] = s.nextInt();
			}
			
			if (n.length == 1) {
				System.out.println("YES");
				continue;
			}
			
			int start = n[0];
			boolean result = true;
				
			for (int j = 1; j < n.length; j++) {
				if (n[j] == start + 1) {
					start = n[j];
				} else if (start == n.length) {
					if (!checkP(n, j-1)) {
						result = false;
						//System.out.println("NO");
					}
					break;
						
				} else {
					result = false;
					//System.out.println("NO");
					break;
				}
			}
			
			if (result) {
				System.out.println("YES");
				//System.out.println("verdikt1: YES");
				continue;
			}
			//System.out.println("verdikt1: NO");
			
//
			int start1 = n[0];
			boolean result1 = true;
				
			for (int j = 1; j < n.length; j++) {
				if (n[j] == start1 - 1) {
					start1 = n[j];
				} else if (n[j] == n.length) {
					if (!checkO(n, j)) {
						result1 = false;
						//System.out.println("NO");
					}
					break;
				} else {
					result1 = false;
					//System.out.println("NO");
					break;
				}
			}
				
			if (result1) {
				System.out.println("YES");
				//System.out.println("verdikt2: YES");
				continue;
			}
			
			System.out.println("NO");
			//System.out.println("verdikt2: NO");
		}
	}
	
	public static boolean checkP (int[] n, int s) {
		if (s == n.length-1 && n[s] < n[0]) return true;
		if (s == n.length-1 && n[s] > n[0]) return false;
		
		for (int i = s+1; i < n.length; i++) {
			if ((n[i] != n[i-1] - 1) || n[i] > n[0]) return false;
		}
		
		return true;
	}
	public static boolean checkO (int[] n, int s /* index */) {
		if (s == n.length-1 && n[0] != n[s]-1) return false;
		if (s == n.length-1 && n[0] == n[s]-1) return true;
		
		for (int i = s+1; i < n.length; i++) {
			if ((n[i] != n[i-1] - 1) || n[i] < n[0]) return false; 
		}
		
		return true;
	}
}
