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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int T = sc.nextInt();
		for(int t = 0; t<T; t++){
		    int len = sc.nextInt();
		    int arr[] = new int[len];
		    int spt = 0;
		    for(int i = 0; i<len; i++){
		        arr[i] = sc.nextInt();
		        if(arr[i] == 1)spt = i;
		    }
		    int k = spt;
		    int num = 1;
		    boolean flag = true;
		    for(int i = 1; i<=len; i++){
		        if(arr[k % len] == num){
		            num++;
		            k++;
		        }
		        else{
		            flag = false;
		            break;
		        }
		    }
		    if(flag)out.println("YES");
		    else{
		        flag = true;
		        k = spt;
		        num = 1;
		        for(int i = 1; i<=len; i++){
		            if(arr[k] == num){
		                k = k == 0 ? len - 1 : k - 1;
		                num++;
		            }
		            else{
		                flag = false;
		                break;
		            }
		        }
		        if(flag)out.println("YES");
		        else out.println("NO");
		    }
		    
		    
		}
		out.flush();
	}
}
