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.*;
import java.util.*;
public class studcircle {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner inputs = new Scanner(System.in);
		int q = inputs.nextInt();
		for(int k=0;k<q;k++) {
			boolean prin = false;
			int n = inputs.nextInt();
			int[] nums = new int[n];
			int oneind=-1;
			
			//places everything and finds the one
			for(int i=0;i<n;i++) {
				nums[i] = inputs.nextInt();
				if(nums[i]==1) {
					oneind = i;
				}
			}
			int spot = 1;
			boolean still = true;
			for(int i=oneind;i<n;i++) {
				if(nums[i]!=spot) {
					still = false;
					break;
				}
				spot++;
			}
			if(still) {
				for(int i=0;i<oneind;i++) {
					if(nums[i]!=spot) {
						still = false;
						break;
					}
					spot++;
				}
			}
			if(still) {
				System.out.println("YES");
				prin = true;
			}
			if(!prin) {
				still = true;
				int tracker = 1;
				for(int i=oneind;i>=0;i--) {
					if(nums[i] != tracker) {
						still  = false;
						break;
					}
					tracker++;
				}
				if(still) {
					for(int i = n-1;i>oneind;i--) {
						if(nums[i] != tracker) {
							still = false;
							break;
						}
						tracker++;
					}
				}
				if(still) {
					System.out.println("YES");
					prin = true;
				}
			}
			if(!prin) {
				System.out.println("NO");
			}
			
		}
	}

}
