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.*;
import java.util.StringTokenizer;

public class Solve {

    public static void main( String[] args ) {

        BufferedReader bis = new BufferedReader(new InputStreamReader(System.in));
        // BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int q = in.nextInt();

        while (q-- > 0){
            int n = in.nextInt();
            int mn = 1500, mx = 0;
            int[] a = new int[n];
            int p = 0;
            int p1 = 0;
            for (int i = 0; i < n; i++){
                a[i] = in.nextInt();
                mx = Math.max(mx, a[i]);
                mn = Math.min(mn, a[i]);
                if (mn == a[i]) p = i;
                if (mx == a[i]) p1 = i;
            }
            boolean ok1 = true, ok2 = true;
            for (int i = p + 1; i < n; i++){
                if (a[i] != mn + 1){
                    ok1 = false;
                    break;
                }mn++;
            }
            if (ok1 == true){
                for (int i = 0; i < p; i++){
                    if (a[i] != mn + 1){
                        ok1 = false;
                        break;
                    }
                }mn++;
            }
            for (int i = p1 + 1; i < n; i++){
                if (a[i] != mx - 1){
                    ok2 = false;
                    break;
                }mx--;
            }
            if (ok2 == true) {
                for (int i = 0; i < p1; i++) {
                    if (a[i] != mx - 1){
                        ok2 = false;
                        break;
                    }mx--;
                }
            }
            if (ok1 == false && ok2 == false) out.print("NO\n");
            else out.print("YES\n");
        }
        out.flush();
    }


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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 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() {
            return Integer.parseInt(next());
        }

    }
}
