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.util.*;
import java.io.*;

public class Program {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        //BufferedReader br = new BufferedReader(new FileWriter("Program.in");
        //StringTokenizer st = new StringTokenizer(br.readLine());
        //PrintWriter pw = new PrintWriter("Program.out");

        int q = sc.nextInt();
        for(int x = 0; x<q; x++){
            int n = sc.nextInt();
            int[] students = new int[n];
            for(int i = 0; i<n; i++){
                students[i] = sc.nextInt();
            }
            int[] cw = new int[n];
            int[] ccw = new int[n];

            int initial = students[0];
            for(int i = 0; i<n; i++){
                if((initial) % (n+1) == 0) {
                    cw[i] = 1;
                    initial++;
                }
                else
                    cw[i] = (initial)%(n+1);
                initial++;
            }

            int initial2 = students[0];
            for(int i = 0; i<n; i++){
                if((initial2) % (n+1) == 0) {
                    ccw[i] = n;
                    initial2 = n;
                }
                else
                    ccw[i] = (initial2) % (n+1);
                initial2 = Math.abs(initial2-1);
            }

            boolean possible = true;
            for(int i = 0; i<n; i++){
                if(cw[i] != students[i] && ccw[i] != students[i]) {
                    possible = false;
                    break;
                }
            }
            //System.out.println(Arrays.toString(cw) + " " + Arrays.toString(ccw));
            if(possible)
                System.out.println("YES");
            else
                System.out.println("NO");
        }
    }
}
