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;

public class ClockDance {

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int t = scanner.nextInt();
    for (int i=0;i<t;i++){
        int n = scanner.nextInt();
        int[] arr = new int[n];
        for (int k =0 ; k<n ; k++){
          arr[k]=scanner.nextInt();
        }
        SEQUENCE sequence = increasingType(arr,0);
        int count = 0;
        for (int k =1 ; k<n ; k++){
          //System.out.println(sequence);
          if(sequence == SEQUENCE.NOT_LINEARLY_INCREASING){
              break;
          }
          sequence = increasingType(arr,k);
        }
        if (sequence == SEQUENCE.NOT_LINEARLY_INCREASING){
          System.out.println("NO");
        }else {
          System.out.println("YES");
        }
      //System.out.println("--");
    }
  }

  enum SEQUENCE{
    INCREASING_LEFT,
    INCREASING_RIGHT,
    NOT_LINEARLY_INCREASING
  }

  public static SEQUENCE increasingType(int[] arr,int index){
      if(arr.length==1||arr.length==0){
        return SEQUENCE.INCREASING_LEFT;
      }

      int right = (index+1)%arr.length;
      int left = ((arr.length+index-1))%arr.length;
    //System.out.println(left+":"+right);
      if (arr[index]-arr[right]==1){
        return SEQUENCE.INCREASING_LEFT;
      }else if(arr[index]-arr[right]==-1){
        return SEQUENCE.INCREASING_RIGHT;
      }
      else if(arr[index]<arr[right]) {
        if (arr[right]-arr[index]==arr.length-1) {
          return SEQUENCE.INCREASING_RIGHT;
        }
      }
      else if(arr[index]-arr[left]==1){
        return SEQUENCE.INCREASING_LEFT;
      }else if(arr[index]-arr[left]==-1){
        return SEQUENCE.INCREASING_RIGHT;
      }else if (arr[left]<arr[index]) {
        if (arr[index]-arr[left] == arr.length-1) {
          return SEQUENCE.INCREASING_RIGHT;
        }
      }

      return SEQUENCE.NOT_LINEARLY_INCREASING;

  }
}


