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;
import java.util.*;

public class codeforces579q3 {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);

        int q = sc.nextInt();
        while (q > 0) {
            int n = sc.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
            }
            if (n == 1) {
                System.out.println("YES");
            }
            
           else if (a[1] - a[0] == 1 || a[0]-a[1] == n-1) {
                if (n == 2) {
                    System.out.println("YES");
                } else {
                    int f=0;
                    int k=0;
                    if(a[0]-a[1]==n-1){
                        f=1;
                    }
                    for (int i = 2; i < n; i++) {
                        if(a[i]-a[i-1]==1){
                            continue;
                        }
                        else if(f==0 && a[i-1]-a[i] == n-1){
                            f=1;
                            continue;
                        }
                        else{
                            System.out.println("NO");
                            k=1;
                            break;
                        }
                        
                    }
                    if(k==0)
                    System.out.println("YES");
                }
            } else if (a[0] - a[1] == 1 || a[1]-a[0] == n-1) {
                if (n == 2) {
                    System.out.println("YES");
                } else {
                    int f=0;
                    int k=0;
                    if(a[1]-a[0]==n-1){
                        f=1;
                    }
                    for (int i = 2; i < n; i++) {
                        if(a[i-1]-a[i]==1){
                            continue;
                        }
                        else if(f==0 && a[i]-a[i-1] == n-1){
                            f=1;
                            continue;
                        }
                        else{
                            System.out.println("NO");
                            k=1;
                            break;
                        }
                        
                    }
                    if(k==0)
                    System.out.println("YES");
                }
            } else {
                System.out.println("NO");
            }
            q--;
        }
        sc.close();
    }
    
}
