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.Scanner;
     
    public class Main {
     
        public static void main(String[] args) {
            Scanner scanner = new Scanner(System.in);
            int q = scanner.nextInt();
            boolean[] result = new boolean[q];
            int n = 0;
            int next = 0;
            int last = 0;
            for (int i = 0; i < q; i++) {
                n = scanner.nextInt();
                if (n == 1 || n == 2) {
                    result[i] = true;
                    continue;
                }
     
                last = scanner.nextInt();
                next = scanner.nextInt();
     
                int diff = next - last;
                if (diff>1) {
                    diff= -1;
                } else if (diff<-1){
                    diff= 1;
                }
     
                int val;
                int expected=0;
     
                for (int j = 2; j < n; j++) {
                    val = next+diff;
                    if (val==0){
                        expected = n;
                    } else if (val == n+1){
                        expected = 1;
                    } else {
                        expected = val;
                    }

                    next = scanner.nextInt();
                    if (next!=expected) {
                        scanner.nextLine();
                        break;
                    }
                }
                if (next == expected) result[i] = true;
            }
            for (int i = 0; i < q; i++) {
                System.out.println(result[i] ? "YES" : "NO");
            }
        }
    }