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
#include <bits/stdc++.h>
using namespace std;

int main(){
   int a;
   while (cin >> a){
        for(int t=0;t<a;t++){
            int b,c,d,e=0;
            cin >> b;
            int arr[b]={0};
            int i;
            for(i=0;i<b;i++){
                cin >> arr[i];
                if(arr[i]==1){
                    c=i;
                }
            }
            if(arr[(c+1)%b]==(arr[c]+1)%b){
                while(arr[c]!=b){
                    if(arr[(c+1)%b]==arr[c]+1){
                        c=(c+1)%b;
                    }else{
                        e=1;
                        break;
                    }
                }
            }
            if(arr[(c-1+b)%b]==(arr[c]+1)%b){
                while(arr[c]!=b){
                    if(arr[(c-1+b)%b]==arr[c]+1){
                        c=(c-1+b)%b;
                    }else{
                        e=1;
                        break;
                    }
                }
            }
            if(e==1){
                cout << "NO" << endl;
            }else{
                cout << "YES" << endl;
            }
        }
   }
   return 0;
}