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.util.*;
import java.io.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class A {

    public static void main(String[] args) throws Exception {
        FastScanner scanner = new FastScanner();

        int T = scanner.nextInt();

        while (T-- != 0) {
            // System.out.println(T);
            int n = scanner.nextInt();
            int[] arr = scanner.nextIntArray();
            ArrayList<Integer> clockwise = new ArrayList <>();
            ArrayList<Integer> counterClockwise = new ArrayList <>();
            for (int i = 0; i < n; i++) {
                clockwise.add(arr[i]);
                counterClockwise.add(arr[i]);
            }

            Collections.sort(counterClockwise, Collections.reverseOrder());

            int i = 0;
            while (counterClockwise.get(0) != arr[i])
                i++;
            int c = 0;


            while (c < counterClockwise.size()) {
                // System.out.println(arr[i] + " " + counterClockwise.get(c));
                if (arr[i] != counterClockwise.get(c)) {
                    break;
                }
                i = i + 1 < counterClockwise.size() ? i + 1 : 0;
                c++;
            }

            if (c >= counterClockwise.size()) {
                System.out.println("YES");
                continue;
            }


            Collections.sort(counterClockwise);

            i = 0;
            while (counterClockwise.get(0) != arr[i])
                i++;
            c = 0;

            while (c < clockwise.size()) {
                // System.out.println("!!!" + arr[i] + " " + counterClockwise.get(c));
                if (arr[i] != counterClockwise.get(c)) {
                    break;
                }
                i = i + 1 < counterClockwise.size() ? i + 1 : 0;
                c++;
            }

            if (c >= counterClockwise.size()) {
                System.out.println("YES");

            } else {
                System.out.println("NO");
            }

        }
    }

    private static class FastScanner {
        private BufferedReader br;

        public FastScanner() { br = new BufferedReader(new InputStreamReader(System.in)); }
        public FastScanner(String input) throws Exception { br = new BufferedReader(new FileReader(input)); }
        public int[] nextIntArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            int[] array = new int[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Integer.parseInt(strings[i]);
            return array;
        }
        public int nextInt() throws IOException { return Integer.parseInt(br.readLine()); }
        public long[] nextLongArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            long[] array = new long[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Long.parseLong(strings[i]);
            return array;
        }
        public ArrayList<Integer> nextIntegerArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Integer> array = new ArrayList<Integer>();
            for (int i = 0; i < strings.length; i++)
                array.add(Integer.parseInt(strings[i]));
            return array;
        }
        public ArrayList<Long> nextLongArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Long> array = new ArrayList<Long>();
            for (int i = 0; i < strings.length; i++)
                array.add(Long.parseLong(strings[i]));
            return array;
        }
        public long nextLong() throws IOException { return Long.parseLong(br.readLine()); }
        public double nextDouble() throws IOException { return Double.parseDouble(br.readLine()); }
        public String nextLine() throws IOException { return br.readLine(); }


        public ArrayList<BigInteger> nextBigIntegers() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<BigInteger> array = new ArrayList<BigInteger>();
            for (int i = 0; i < strings.length; i++)
                array.add(BigInteger.valueOf(Long.valueOf(strings[i])));
            return array;
        }
    }
}
