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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 *
 */
public class CircleOfStudents {

    public static void main(String[] args) {
        
        FastReader in = new FastReader();
        
        int tcase = in.nextInt();
        
        for (int i = 0; i < tcase; i++) {
            
            int s = in.nextInt();
            
            int[] array = new int[s];

            for (int j = 0; j < s; j++) {
                
                int val = in.nextInt();
                array[j]=val;
           
            }
            
            boolean found = false;
            int start = -1;
            int next = 0;
            int count1 = s, count2 = s;
            
            for (int j = 0; j < s; j++) {
 
                start = j;
                next = (j+1);
                
                for (int k = 0; k < s; k++) {
                    start %=s;
                    next %=s;
                    if (array[next]==array[start]+1)
                        count1--;
                    if (array[next]==array[start]-1)
                        count2--;
                    
                    start++;
                    next++;         
                }
                
                if (count1 == 1 ||count2==1){ 
                    System.out.println("YES");
                    found = true;
                    break;
                }
                count1 = s;
                count2 = s;
                        
            }
            
            if (found == false)
                System.out.println("NO");
        }
        
    }

    public static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String string = "";
            try {
                string = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return string;
        }

    }

}
