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 Main {

	public static void main(String[] args) throws Exception{
		BufferedReader  jk =  new BufferedReader(new InputStreamReader( System.in))  ; 
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)) ; 
		StringTokenizer ana = new StringTokenizer(jk.readLine()) ;
		int q  =Integer.parseInt(ana.nextToken()) ; 
		for(int j=0 ; j<q ;j++)
		{
			ana = new StringTokenizer(jk.readLine()) ;
			int n = Integer.parseInt(ana.nextToken()) ; 
			if(n==1) out.println("YES");
			else
			{
				ana = new StringTokenizer(jk.readLine()) ; 
				int t[] = new int[2*n] ; 
				for(int i=0 ; i<n ;i++)
				{
					t[i]= Integer.parseInt(ana.nextToken()) ; 
				}
				for(int i=n ;i<2*n ;i++)
				{
					t[i] = t[i%n] ; 
				}
				boolean t1 = true ; boolean t2= true; 
				for(int i=0 ; i<2*n-1 ;i++)
				{
					int cur = t[i+1] ; int next= t[i]+1 ; 
					if(next>n) next%=n ; 
					if(cur!=next) t1 = false ; 
				}
				for(int i=2*n-1 ; i>0 ;i--)
				{
					int cur = t[i-1] ; int next= t[i]+1 ; 
					if(next>n) next%=n ; 
					if(cur!=next) t2 = false ; 
				}
				if(t1 || t2) out.println("YES");
				else out.println("NO");
			}
			


		}

		out.flush();
	}
}


