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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int q = Integer.parseInt(br.readLine());
        while(q-- >0){
            int n = Integer.parseInt(br.readLine());
            StringTokenizer st = new StringTokenizer(br.readLine());
            int[] array = new int[n];
            for(int i=0;i<n;i++){
                array[i] =  Integer.parseInt(st.nextToken());
            }
            if(n==1){
                pw.println("YES");
                continue;
            }
            boolean i=false,d=false;
            if(array[1] == array[0]+1){
                i = true;
            } else {
                d= true;
            }
            int index =1;
            if(i){
                while(index < n){
                    if(array[index] == array[index-1] + 1){
                        index++;
                    }else{
                        break;
                    }
                }
                if(index==n){
                    pw.println("YES");
                } else{
                    index++;
                    while(index < n){
                        if(array[index] == array[index-1] + 1){
                            index++;
                        }else{
                            break;
                        }
                    }
                    if(index==n){
                        pw.println("YES");
                    }else{
                        pw.println("NO");
                    }
                }
            } else{
                while(index < n){
                    if(array[index] == array[index-1] - 1){
                        index++;
                    }else{
                        break;
                    }
                }
                if(index==n){
                    pw.println("YES");
                } else{
                    index++;
                    while(index < n){
                        if(array[index] == array[index-1] - 1){
                            index++;
                        }else{
                            break;
                        }
                    }
                    if(index==n){
                        pw.println("YES");
                    }else{
                        pw.println("NO");
                    }
                }
            }
        }
        pw.close();
    }
}
