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.*;
    import java.lang.*;
    import java.io.*;
    import java.io.BufferedInputStream;
    import java.io.IOException;
    public final class codeforces {
        public static void main(String[]args)
        {
            Scanner scan = new Scanner(System.in);
                    int q  = scan.nextInt();
            int k = 0;
            //int m  = scan.nextInt();
            //scan.nextLine();
            while(k++ < q)
            {
                int i = 0;
                int n  = scan.nextInt();
                int[] a = new int[n];
                boolean dance = true ;
                while(i < n) 
                    a[i++] = scan.nextInt();
                int prev = a[0];
                i = 1;
                while(i < n)
                {
                    //System.out.println(a[i] + " " + prev + " "+ (a[i] != prev+1));
                    if(a[i] == prev+1 ||  a[i] == prev-1)
                    {
                        prev = a[i];
                        i++;
                        continue;
                    }
                    else if((a[i] == n && prev == 1) || (a[i] == 1 && prev == n) ||
                        (a[i] == (prev +1)/n) || (a[i] == (prev -1)/n) )
                        {   
                            prev = a[i];
                            i++;
                            continue;
                        }
                    else
                    {
                        dance = false;
                        break;
                    }
                }
                if(dance == true)
                    System.out.println("YES");
                else
                    System.out.println("NO");
            }
        }
    }