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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

import java.io.BufferedReader;



public class Main{

    public static void main(String[] args) throws IOException {

        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int q = sc.nextInt();

        for (int i = 0; i < q; i++) {
            int n  = sc.nextInt();

            int[] a = new int[n];
            int start = 0;
            for (int j = 0; j < n; j++) {
                a[j] = sc.nextInt();
                if (a[j] == 1)
                    start = j;
            }

            boolean clockwise = true;
            boolean counterclockwise = true;

            for (int j = (start +1)%n; true; j = ++j%n) {
                int next = (j == n-1?0:j+1);
                if (a[next] == 1) break;
                if (a[next]-a[j] != 1) clockwise = false;
            }

            for (int j = (start == 0?n-1:start-1); true; j = (j== 0?n-1:j-1)) {
                int next = (j == 0?n-1:j-1);
                if (a[next] == 1) break;
                if (a[next]-a[j] != 1) counterclockwise = false;
            }

            if (clockwise || counterclockwise) out.println("YES");
            else out.println("NO");
            }



        out.flush();
    }

}



class Scanner {
    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream system) {
        br = new BufferedReader(new InputStreamReader(system));
    }

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

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

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

    public char nextChar() throws IOException {
        return next().charAt(0);
    }

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

    public boolean ready() throws IOException {
        return br.ready();
    }

    public void waitForInput() throws InterruptedException {
        Thread.sleep(3000);
    }


}

