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.File;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Locale;
import java.util.Scanner;

public class Main {
    private int[][] arr;
    private int[] path;
    private boolean[][] res;

    private void run() {
        int q = in.nextInt();
        while (--q >= 0) {
            int n = in.nextInt();
            int[] arr = new int[n];
            int one = 0;
            for (int i = 0; i < n; ++i) {
                arr[i] = in.nextInt();
                if (arr[i] == 1) {
                    one = i;
                }
            }

            if (checkArray(arr, one)) {
                out.println("YES");
            } else {
                out.println("NO");
            }

        }
    }

    private boolean checkArray(int[] arr, int one) {
        int len = arr.length;
        if (len == 1) {
            return true;
        }
        boolean forward = arr[one] +1 == arr[(one + 1) % len];
        if (forward) {
            int cp = one;
            int ncp = (cp + 1) % len;
            while ( ncp != one ) {
                if (arr[ncp] - arr[cp] != 1) {
                    return false;
                }
                cp = ncp;
                ncp = (cp + 1) % len;
            }
        } else {
            int cp = one;
            int ncp = (cp - 1 + len) % len;
            while ( ncp != one ) {
                if (arr[ncp] - arr[cp] != 1) {
                    return false;
                }
                cp = ncp;
                ncp = (cp - 1+ len) % len;
            }
        }

        return true;
    }

    public static void main(String[] args) throws IOException {
        new Main().prepare();
    }

    private PrintWriter out;
    private Scanner in;

    private void prepare() throws IOException {
        if ("true".equals(System.getProperty("ONLINE_JUDGE"))) {
            in = new Scanner(System.in);
        } else {
            in = new Scanner(new File("src/"+this.getClass().getPackage().getName().replace('.', '/')+"/input.txt"));
        }
        out = new PrintWriter(System.out);
        in.useLocale(new Locale("US"));
        run();
        out.println();
        out.flush();
    }
}