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.*;
public class completing_projects
{
	public static void main(String[] args) 
	{
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        while (t-->0)
        {
        	int n = s.nextInt();
        	int[] arr = new int[n];
        	int st = 0;
        	for (int i=0;i<n;i++)
        	{
        		arr[i] = s.nextInt();
        		if (arr[i]==1)
    			{
    			st = i;
    			}
        	}
        	if (n==1)
        	{
        		System.out.println("YES");
        		continue;
        	}
        	int p = 1;
        	boolean iscir = true;
        	boolean clk = arr[1]-arr[0]==1||arr[0]-arr[n-1]==1?true:false;
        	int rep = n-1;
        	while (rep-->0)
        	{
        		if (clk)
        		st++;
        		else
        		st--;
        		if (st==n)
        			st = 0;
        		else if (st==-1)
        			st = n-1;
        		if (arr[st]==p+1)
        			p = arr[st];
        		else
    			{
    			iscir = false;
    			break;
    			}
        	}
        	if (iscir)
        		System.out.println("YES");
        	else
        		System.out.println("NO");
        }
        s.close();
	}
}