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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class P1 {
    public static void main(String[] bb) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while (t-- > 0) {
            int n = Integer.parseInt(br.readLine());
            if (n == 1) {
                System.out.println("YES");
                continue;
            }
            int arr[] = new int[n];
            StringTokenizer tokens = new StringTokenizer(br.readLine());
            int start = 0;
            for (int i = 0; i < arr.length; i++) {
                int num = Integer.parseInt(tokens.nextToken());
                if (num == 1) {
                    start = i;
                }
                arr[i] = num;
            }
            int next = 1;
            if ((start + 1 < arr.length && arr[start + 1] == 2) ||
                    (start + 1 == arr.length && arr[0] == 2)) {
                while (next <= n) {
                    if (arr[start] == next) {
                        if (start + 1 == arr.length) {
                            start = 0;
                        } else {
                            start++;
                        }
                        next++;
                        if (next == n + 1) {
                            System.out.println("YES");
                            break;
                        }
                    } else {
                        System.out.println("NO");
                        break;
                    }
                }
            } else if ((start - 1 > -1 && arr[start - 1] == 2) ||
                    (start - 1 == -1 && arr[arr.length - 1] == 2)) {
                if (arr[start] == next) {
                    while (next <= n) {
                        if (arr[start] == next) {
                            if (start - 1 == -1) {
                                start = arr.length - 1;
                            } else {
                                start--;
                            }
                            next++;
                            if (next == n + 1) {
                                System.out.println("YES");
                                break;
                            }
                        } else {
                            System.out.println("NO");
                            break;
                        }
                    }
                }
            } else {
                System.out.println("NO");
            }
        }
    }
}































