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;

/**
 *
 * @author s.svorovskij
 */
public class JavaApplication17 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int q = in.nextInt();
        for (int i = 0; i < q; i++) {
            int n = in.nextInt();
            int arr[] = new int[n];
            for (int j = 0; j < n; j++) {
                arr[j] = in.nextInt();
            }
            int narr[] = new int[3 * n];
            for (int j = 0; j < n; j++) {
                narr[j] = arr[j];
            }
            for (int j = 0; j < n; j++) {
                narr[n + j] = arr[j];
            }
            for (int j = 0; j < n; j++) {
                narr[2 * n + j] = arr[j];
            }
            //right 
            int rigthM = 0;
            int rightC = 0;
            for (int j = 1; j < 3 * n; j++) {
                if (narr[j] - narr[j-1] == 1) {
                    rightC++;
                } else {
                    if (rigthM < rightC) {
                        rigthM = rightC;
                    }
                    rightC = 0;
                }
            }
            
            //left 
            int leftM = 0;
            int leftC = 0;
            for (int j = 3*n - 2; j >= 0; j--) {
                if (narr[j + 1] - narr[j] == -1) {
                    leftC++;
                } else {
                    if (leftM < leftC) {
                        leftM = leftC;
                    }
                    leftC = 0;
                }
            }
            
            if (rigthM == n - 1 || leftM == n - 1) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
        }
        // TODO code application logic here
    }

}