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.lang.*;
import java.util.*;

public class CircleOfStudents {
    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        TaskC solver = new TaskC(in, out);
        solver.solve();
        out.close();
    }

    static class TaskC {
        FastReader in;
        PrintWriter out;

        public TaskC(FastReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve() {
            int q = in.nextInt();

            while (q-- > 0) {
                int n = in.nextInt();
                int[] array = in.nextIntArray(n);

                boolean isCircular = true;
                boolean isCircular2 = true;

                if (n > 1) {
                    int minIndex = -1;
                    int minValue = Integer.MAX_VALUE;

                    for (int i = 0; i < n; i++) {
                        if (array[i] < minValue) {
                            minValue = array[i];
                            minIndex = i;
//                            out.println("Current Value - " + array[i] + ", MIN VALUE - " + minValue + ", MIN INDEX - " + minIndex);
                        }
                    }

                    int l = 1;
                    for (int i = minIndex; i < minIndex + n; i++) {
                        if (array[i%n] != l) {
                            isCircular = false;
                            break;
                        }
                        l++;
                    }

                    if (!isCircular) {
                        int k = n;
//                        out.println(minIndex);
                        for (int i = minIndex+1; i <= minIndex + n; i++) {
//                            out.println((i%n) + " --- " + k);
                            if (array[i%n] != k) {
                                isCircular2 = false;
                                break;
                            }
                            k--;
                        }
                    }
                }

                out.println(((isCircular || isCircular2) ? "YES" : "NO"));
            }
        }
    }

    private static int min(int a, int b) {
        return a < b ? a : b;
    }

    private static int max(int a, int b) {
        return a > b ? a : b;
    }

    private static int min(ArrayList<Integer> list) {
        int min = Integer.MAX_VALUE;
        for (int el : list) {
            if (el < min) {
                min = el;
            }
        }
        return min;
    }

    private static int max(ArrayList<Integer> list) {
        int max = Integer.MIN_VALUE;
        for (int el : list) {
            if (el > max) {
                max = el;
            }
        }
        return max;
    }

    private static int min(int[] list) {
        int min = Integer.MAX_VALUE;
        for (int el : list) {
            if (el < min) {
                min = el;
            }
        }
        return min;
    }

    private static int max(int[] list) {
        int max = Integer.MIN_VALUE;
        for (int el : list) {
            if (el > max) {
                max = el;
            }
        }
        return max;
    }

    private static void fill(int[] array, int value) {
        for (int i = 0; i < array.length; i++) {
            array[i] = value;
        }
    }


    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }
    }
}