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<iostream>
#include<bits/stdc++.h>

using namespace std;

int countDistinct(int arr[], int n) 
{ 
    // First sort the array so that all 
    // occurrences become consecutive 
    sort(arr, arr + n); 
  
    // Traverse the sorted array 
    int res = 0; 
    for (int i = 0; i < n; i++) { 
  
        // Move the index ahead while 
        // there are duplicates 
        while (i < n - 1 && arr[i] == arr[i + 1]) 
            i++; 
  
        res++; 
    } 
  
    return res; 
} 

int main()
{
	long long int n;
	cin>>n;
	
	for (int i=0; i<n; i++)
	{
		int queries;
		cin>>queries;
		
		
		
		
		int array[queries] = {0};
		int array1[queries]= {0};
		for (int j=0; j<queries; j++)
		
		{
			cin>>array[j];
		}
		for (int j=0; j<queries; j++)
		{
			if(j==0) array1[j] = array[j] - array[queries-1];
			else array1[j] = array[j] - array[j-1];
		}
		int distinct = countDistinct(array1, queries);
		if (distinct==2) cout<<"YES"<<endl;
		else cout<<"NO"<<endl;
	
	}
	return 0;
}
