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.*;

/**
 * Created by Ayushi on 13/08/2019.
 */

public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
        String[] temp = r.readLine().split(" ");
        int q = Integer.parseInt(temp[0]);
        for (int i = 0; i < q; i++) {
            temp = r.readLine().split(" ");
            int n = Integer.parseInt(temp[0]);
            int[] a = new int[n];
            temp = r.readLine().split(" ");
            int x, y;
            x = y = 0;
            for (int j = 0; j < n; j++) {
                a[j] = Integer.parseInt(temp[j]);
                if (a[j] == n) x = j;
                if (a[j] == 1) y = j;
            }
            boolean cw, acw;
            cw = acw = true;
            for (int l = y; l < n-1 && cw; l++) {
                if (a[l] > a[l+1]) cw = false;
                //System.out.println("cw! = " + cw);
            }
            if (y != 0 && a[n-1] > a[0]) cw = false;
            //System.out.println("cw = " + cw);
            for (int l1 = 0; l1 < y-1 && cw; l1++) {
                if (a[l1] > a[l1+1]) cw = false;
                //System.out.println("cw = " + cw);
            }

            for (int k = x; k < n-1 && acw; k++) {
                if (a[k] < a[k+1]) acw = false;
            }
            if (x != 0 && a[n-1] < a[0]) acw = false;
            for (int k1 = 0; k1 < x-1 && acw; k1++) {
                if (a[k1] < a[k1+1]) acw = false;
            }

            //System.out.println("cw = " + cw);
            //System.out.println("acw = " + acw);
            System.out.println((cw || acw) ? "YES" : "NO");
        }
        r.close();
    }
}
