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.BufferedReader;
import java.io.InputStreamReader;

public class Students {

    public static void main(final String[] args) throws Exception {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	int q = Integer.parseInt(br.readLine());
	for (int i = 0; i < q; i++) {
	    int n = Integer.parseInt(br.readLine());
	    String[] aString = br.readLine().split(" ");
	    if (n == 1) {
		System.out.println("YES");
		continue;
	    }
	    boolean alreadyPrint = false;
	    int type = 0;
	    int cur = Integer.parseInt(aString[0]);
	    int first = cur;
	    for (int j = 1; j < aString.length; j++) {
		int next = Integer.parseInt(aString[j]);
		if (type == 0) {
		    if (cur == 1 && next == n) {
			type = 1;
		    } else if (cur == n && next == 1) {
			type = -1;
		    } else if (Math.abs(cur - next) != 1) {
			System.out.println("NO");
			alreadyPrint = true;
			break;
		    } else {
			type = cur - next;
		    }
		} else if (cur != next + type) {
		    if ((type == -1 && (cur != 1 || next != n)) || (type == 1 && (cur != n || next != 1))) {
			System.out.println("NO");
			alreadyPrint = true;
			break;
		    }
		}
		cur = next;
	    }
	    if (!alreadyPrint) {
		if ((cur != first + type) && ((type == -1 && (first != 1 || cur != n)) || (type == 1 && (first != n || cur != 1)))) {
		    System.out.println("NO");
		    continue;
		}
		System.out.println("YES");
	    }

	}
    }

}
