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.*;
public class MyScanner_
{
    static MyScanner sc = new MyScanner();
    static PrintWriter pw = new PrintWriter(System.out,true);
    static StringBuilder sb = new StringBuilder();
    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        MyScanner()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String nextLine()throws IOException
        {
            return br.readLine();
        }
        String ne() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        int ni() throws IOException
        {
            return Integer.parseInt(ne());
        }
        long nl() throws IOException
        {
            return Long.parseLong(ne());
        }
        double nd() throws IOException
        {
            return Double.parseDouble(ne());
        }
    }
    public static void main(String[] args) throws IOException {
        new Thread(null, null, "Rahsut", 1 << 25) {
            public void run() {
                try {
                    F___k();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static void F___k() throws IOException {
        //write Code here
        int q = sc.ni();
        while(q-->0) {
            int n = sc.ni();
            int arr[]= new int[n];
            for(int i =0;i<n;i++)
                arr[i]= sc.ni();
            boolean bool = true;
            for(int i =0;i<n-1;i++) {
                int x = Math.abs(arr[i]-arr[i+1]);
                //System.out.println(x);
                if(x!=1 && x!=n-1) {
                    bool = false;
                    break;
                }
            }
            if(bool)
                sb.append("YES\n");
            else
                sb.append("NO\n");
        }
        pw.println(sb);
        pw.flush();
        pw.close();
    }

}