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
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
//package Practice_1100;

import java.io.*;

/**
 *
 * @author Akhilesh
 */
public class A1203 {
    public static void main(String[] args) throws IOException {
        BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));
        
        int test = Integer.parseInt(scan.readLine().trim());
        
        test:
        while (test-- > 0) {
            String str[] = scan.readLine().split("\\s+");
            int n = Integer.parseInt(str[0]);
            
            int arr[] = new int[n];
            str = scan.readLine().split("\\s+");
            int index = 0;
            
            if(str.length == 1){
                System.out.println("YES");
                continue;
            }
            
            for(int i = 0; i < n; i++){
                arr[i] = Integer.parseInt(str[i]);
                if(arr[i] == 1){
                    index = i;
                }
            }
            
            int add = 0;
            
            if( arr[ (index + 1 + n)%n ] == 2){
                add = 1;
            }else
                if( arr[ (index - 1 + n)%n ] == 2){
                    add = -1;
                }else{
                    System.out.println("NO");
                    continue;
                }
                    
            int i = (index + add + n)%n, j = index;
            while( i != index ){
                if(arr[i] != arr[j] + 1){
                    System.out.println("NO");
                    continue test;
                }
                
                j = i;
                i = (i + add + n)%n;
            }
            
            System.out.println("YES");
        }
    }    
}
