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
//package com.codefarm.codeforces;

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

public class ValidCircle {
    public static void main(String[] args) {
        InputReader reader = new InputReader();

        int Q = reader.nextInt();

        for(int q=0; q<Q; q++) {
            int N = reader.nextInt();
            int[] arr = new int[N];
            for(int i=0; i<N; i++) {
                arr[i] = reader.nextInt();
            }

            int index = -1, indexC=-1;
            for(int i=0; i<N; i++) {
                if (arr[i] == 1) {
                    index = i;
                    indexC = i;
                }
            }
            boolean possible = true;
            int count = 0;
            while (count < N) {
                count++;
                if (count != arr[index]) {
                    possible = false;
                    break;
                }
                index = (index+1)%N;
            }

            if (possible) {
                System.out.println("YES");
                continue;
            }

            count = 0;
            possible = true;
            while (count < N) {
                count++;
                if (count != arr[indexC]) {
                    possible = false;
                    break;
                }
                indexC = (indexC-1+N)%N;
            }

            if (possible)
                System.out.println("YES");
            else System.out.println("NO");

        }
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }


        public int nextInt() {
            String nxt = next();
//            System.out.println(nxt);
            return Integer.parseInt(nxt);
        }

        public long nextLong() {
            String nxt = next();
//            System.out.println(nxt);
            return Long.parseLong(nxt);
        }

    }
}
