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.*;
import java.util.*;
import java.lang.*;
public class Test {
    public static void main(String args[])throws Exception{
        Scanner sc = new Scanner(System.in);
        int q=sc.nextInt();
        while(q>0) {
            q--;

            int n = sc.nextInt();
            int arr[] = new int[n];
            int brr[] = new int[2*n];
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
            }
            int i = 0;
            for (int j = 0; j < n; j++) {
                brr[i] = arr[j];
                i++;
            }
            for (int j = 0; j < n; j++) {
                brr[i] = arr[j];
                i++;
            }
            int k = 1;
            int flag = 0;
            int found = 0;
            for (int j = 0; j < 2 * n; j++) {
                if (brr[j] == 1) {
                    flag = 1;
                }
                if (flag == 1) {
                    if (brr[j] == k) {
                        if(k==n)break;
                        k++;
                    } else {
                        found=1;
                        break;
                    }
                }
            }
            if(found==1){
                k = n;
                flag = 0;
                found = 0;
                for (int j = 0; j < 2 * n; j++) {
                    if (brr[j] == n) {
                        flag = 1;
                    }
                    if (flag == 1) {
                        if (brr[j] == k) {
                            if(k==1)break;
                            k--;
                        } else {
                            found=1;
                            break;
                        }
                    }
                }
                if(found==1){
                    System.out.println("NO");
                }
                else{
                    System.out.println("YES");

                }

            }
            else{
                System.out.println("YES");
            }
        }
    }
    }
    class Value {
        public int a,b;
        public Value(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    class SortA implements Comparator<Value>{
        public int compare(Value o1, Value o2) {
            Value a=(Value)o1;
            Value b=(Value)o2;
            if(a.a > b.a){
                return 1;
            }
            return -1;
        }
    }
    class SortB implements Comparator<Value>{
    public int compare(Value o1, Value o2) {
        Value a=(Value)o1;
        Value b=(Value)o2;
        if(a.b < b.b){
            return 1;
        }
        if(a.a < b.a && a.b==b.b){
            return 1;
        }
        return -1;
    }
}

