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.util.*;

/*CODE BY SHIKHAR TYAGI*/
public class A {
    public static void main(String args[]) {
        FastScanner scn = new FastScanner();

        int t = scn.nextInt();
        while (t-- > 0) {
            int n = scn.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; ++i) {
                a[i] = scn.nextInt();
            }
            if (clockwise(a, n) || anticlockwise(a, n)) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
        }
    }

    private static boolean clockwise(int[] a, int n) {
        if (n == 1) {
            return true;
        }
        int i = 1;
        int cur = a[0];
        while (i < a.length && nextc(cur, n) == a[i]) {
            cur = a[i];
            i++;
        }
        if (i == a.length)
            return true;
        else
            return false;
    }

    private static int nextc(int cur, int n) {
        if (cur == n) {
            return 1;
        }
        return cur + 1;
    }

    private static int nextcc(int cur, int n) {
        if (cur == 1) {
            return n;
        }
        return cur - 1;
    }

    private static boolean anticlockwise(int[] a, int n) {
        if (n == 1) {
            return true;
        }
        int i = 1;
        int cur = a[0];
        while (i < a.length && nextcc(cur, n) == a[i]) {
            cur = a[i];
            i++;
        }
        if (i == a.length)
            return true;
        else
            return false;
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

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

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

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

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

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