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 java.math.*;
 
public class A {
 
    public static void main(String[] args) throws Exception {
        // FileInputStream inputStream = new FileInputStream("input.txt");
        // FileOutputStream outputStream = new FileOutputStream("output.txt");
 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
         
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
 
        Solver solver = new Solver();     
        // int t = in.nextInt();
        int t = 1;
        for (int i = 0 ; i < t ; i++) {
            solver.solve(1, in, out);
        }
                 
        out.close();
    }
 
    static class Solver {
 
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int g = in.nextInt();
            for (int q = 0; q < g; q++) {
                int n = in.nextInt();
                Integer[] a = new Integer[n+1];
                int j = 0;
                for (int i = 1; i <= n; i++) {
                    a[i] = in.nextInt();
                    if (a[i] == 1) j = i;
                }

                int c = 0; 
                int k = 0;
                if (j == n) k = 1; else k = j+1;
                int s = 2;
                for (int f = 1; f <= n-1; f++) {
                    if (a[k] != s) {
                        c = 1; 
                        break;
                    }
                    if (k == n) k = 1; else k++;
                    if (s == n) s = 1; else s++;
                }
                if (c == 0) { out.println("YES"); continue; }
                c = 0;
                if (j == 1) k = n; else k = j-1;
                s = 2;
                for (int f = 1; f <= n-1; f++) {
                    if (a[k] != s) {
                        c = 1;
                        break;
                    }
                    if (k == 1) k = n; else k--;
                    if (s == n) s = 1; else s++;
                }
                if (c == 0) out.println("YES"); else out.println("NO");
            }
        }
 
 
    }
 
    
             
 
    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());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }
}