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
// loltyleronedotcomdiscountcodealpha
import java.io.*;
import java.util.*;
import java.lang.Math;

public class Main {

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e){e.printStackTrace();}
        }

        public String next() {
            if (st.hasMoreTokens()) return st.nextToken();
            try {st = new StringTokenizer(br.readLine());}
            catch (Exception e) {e.printStackTrace();}
            return st.nextToken();
        }

        public int nextInt() {return Integer.parseInt(next());}

        public long nextLong() {return Long.parseLong(next());}

        public double nextDouble() {return Double.parseDouble(next());}

        public String nextLine() {
            String line = "";
            if(st.hasMoreTokens()) line = st.nextToken();
            else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
            while(st.hasMoreTokens()) line += " "+st.nextToken();
            return line;
        }
    }

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        final int MOD = 1000000007;

        int q = sc.nextInt();
        while(q-->0) {
            int n = sc.nextInt();
            int[] a = new int[n];
            for(int i=0;i<n;i++) a[i] = sc.nextInt();
            int last = a[0];
            boolean ok = true;
            for(int i=1;i<n;i++) {
                int next = a[i];
                if(last == n) {
                    last = 0;
                }
                if(next == last + 1) {
                    last = next;
                    continue;
                }
                ok = false;
                break;
            }
            if(ok) {
                pw.println("YES");
                continue;
            }
            last = a[0];
            ok = true;
            for(int i=1;i<n;i++) {
                int next = a[i];
                if(last == 1) {
                    last = n + 1;
                }
                if(last - 1 == next) {
                    last = next;
                    continue;
                }
                ok = false;
                break;
            }
            pw.println(ok ? "YES" : "NO");
        }

        pw.close();
    }
}

// ceil(a/b) = (a+b-1)/b
// PRO TIP: THE BEST ANSWER IS THE RIGHT ANSWER