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.StreamTokenizer;

public class Main {
    private static StreamTokenizer in;

    public static void main(String[] args) throws IOException{
        in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        int req = nextInt();
        int n; //Количество студентов
        int[] pos; //позиции студентов
        boolean rightDelay;
        boolean revDelay;
        for (int w = 0; w < req; w++) {
            rightDelay = true;
            revDelay = true;

            n = nextInt();
            pos = new int[n];
            pos[0] = nextInt();

            for (int i = 1; i < n; i++){
                pos[i] = nextInt();
                if (pos[i] != pos[i - 1] + 1 && !(pos[i] == 1 && pos[i - 1] == n)) { // 1 2 3 4 5 // 3 4 5 1 2
                    rightDelay = false;
                }
                if (pos[i] != pos[i - 1] - 1 && !(pos[i] == n && pos[i - 1] == 1)) { // 5 4 3 2 1 // 2 1 5 4 3
                    revDelay = false;
                }
            }

            if (pos[n - 1] != pos[0] - 1 && !(pos[0] == 1 && pos[n - 1] == n)) { // 1 2 3 4 5 or 5 1 2 3 4
                rightDelay = false;
            }
            if (pos[0] != pos[n - 1] - 1 && !(pos[0] == n && pos[n - 1] == 1)) { // 5 4 3 2 1 or 3 2 1 5 4
                revDelay = false;
            }

            if (revDelay || rightDelay) {
                System.out.println("YES");
            } else {System.out.println("NO");}
        }

    }

    private static int nextInt() throws IOException {
        in.nextToken();
        return (int)in.nval;
    }
}
