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.math.BigInteger;
import java.util.*;


public class Main {

    private static List<List<Integer>> subsets;
    private static int count = 0;
    private static BigInteger thirteen = new BigInteger("13");
    private static BigInteger five = new BigInteger("5");
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        InputReader.OutputWriter out = new InputReader.OutputWriter(outputStream);



        int q = in.nextInt();
        while (q-->0) {
            int n = in.nextInt();
            int [] a = new int[n];
            for (int i = 0; i < a.length; i++) {
                a[i] = in.nextInt();
            }

            if(isReverse(a) || istraight(a)) {
                out.println("YES");
            }
            else {
                out.println("NO");
            }
        }

       /* int n = in.nextInt();
        long [] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = in.nextLong();
        }
        long gcd = a[0];
        for (int i = 1; i < a.length; i++) {
            gcd=_gcd(a[i],gcd);
        }
        int count = 0;
        for (int i = 1; i*i <=gcd; i++) {
            if(gcd%i==0) {
                count++;
                if(i*i!=gcd) {
                    count++;
                }
            }
        }

        out.println(count);*/
        out.flush();
    }
    static long _gcd(long a,long b) {
        return b == 0 ? a : _gcd(b,a%b);
    }
    static boolean isReverse(int [] a) {
        for (int i = 0; i < a.length; i++) {
            if(a[i]!=1) {
                if(i==0) {
                    if(a[a.length - 1] - a[0]!=1) return false;
                }
                else if(i!=a.length-1) {
                    if(a[i]-a[i+1]!=1) return false;
                }
                else {
                    if(a[a.length-1]-a[0]!=1) return false;
                }
            }
        }
        return true;
    }
    static boolean istraight(int [] a) {
        int n = a.length;
        for (int i = 0; i < a.length; i++) {
            if(a[i]!=1) {
                if (i == 0) {
                    if (a[a.length - 1] != a[i] - 1) return false;
                } else if (i != a.length - 1) {
                    if (a[i - 1] != a[i] - 1) return false;
                } else {
                    if (a[0] - a[a.length - 1] != 1 && a[i]!=n) return false;
                }
            }
        }
        return true;
    }
    static void swap(Job[] jobs, int i,int j) {
        Job temp = jobs[i];
        jobs[i] = jobs[j];
        jobs[j] = temp;
    }
    static int binarySearch(Job[] jobs, int index, int reward, int day) {
        int lo = index;
        int hi = jobs.length - 1;
        while (lo<=hi) {
            int med = lo + (hi-lo)/2;
            if(jobs[med].getDay() < day) return med;
            if (reward > jobs[med].getReward()) {
                hi = med - 1;
            }
            else {
                lo = med + 1;
            }
        }
        return -1;
    }

}
class Job {
    private int reward;
    private int day;

    public int getDay() {
        return day;
    }

    public int getReward() {
        return reward;
    }
    
    public Job(int day, int reward) {
        this.reward = reward;
        this.day = day;
    }

    @Override
    public String toString() {
        return day + " " + reward;
    }
}
class InputReader extends BufferedReader {
    StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
        super(new InputStreamReader(inputStream), 32768);
    }

    public InputReader(String filename) {
        super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(readLine());
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
        return tokenizer.nextToken();
    }
    public Integer nextInt() {return Integer.valueOf(next());}
    public Long nextLong() {return  Long.valueOf(next());}
    public Double nextDouble() {return Double.valueOf(next());}

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }
    }
}