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.*;
 
public class mishra {
 
    public static void main(String args[]) {
        Scanner ob = new Scanner(System.in);
        int T = ob.nextInt();
        for (int i = 0; i < T; i++) {
            int n = ob.nextInt();
            Integer[] arr = new Integer[n];
            for (int j = 0; j < n; j++) {
                arr[j] = ob.nextInt();
            }
            String a = "YES";
            int min = Collections.min(Arrays.asList(arr));
            int index1 = Arrays.asList(arr).indexOf(min);
            int max = Collections.max(Arrays.asList(arr));
            int index2 = Arrays.asList(arr).indexOf(max);
            if(n<=3)
            {System.out.println("YES");
            break;}
            if (index1 - index2 != 1 && index2 - index1 != (n - 1) && index1 - index2 != -1 ) {
                System.out.println("NO");
                break;
            } else {
                int j = 0, k = 0;
                if (index2 - index1 == n - 1) {
                   System.out.println("aaa");
                    while (j < n - 1) {
                        if (arr[j] > arr[j + 1]) {
                            a = "N0";
                        
                        }
                        j++;
                    }
                }
 
                else if (index1 > index2) {
                   System.out.println("bbb");
                    j = index1;
                    k = index2;
                    while (j < n - 1 || k > 0) {
                        if (j < n - 1) {
                            if (arr[j] > arr[j + 1]) {
                                a = "NO";
                                break;
                            }
                            j++;
                        }
                        if (k > 0) {
                            if (arr[k] < arr[k - 1]) {
                                a = "NO";
                                break;
                            }
                            k--;
                        }
                    }
                } else {
                   System.out.println("ccc");
                    k = index1;
                    j = index2;
                    while (j < n - 1 || k > 0) {
                        if (j < n - 1) {
                            if (arr[j] < arr[j + 1]) {
                                a = "NO";
                                break;
                            }
                            j++;
                        }
                        if (k > 0) {
                            if (arr[k] > arr[k - 1]) {
                                a = "NO";
                                break;
                            }
                            k--;
                        }
                    }
                }
                System.out.println(a);
            }
           
        }
        ob.close();
    }
}