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 A {
	public static void main(String[] arg) throws IOException{
		Reader.init(System.in);
		int t=Reader.nextInt();
		while (t-->0) {
			int n=Reader.nextInt();
			int[] p=new int[n];
			for (int i = 0;i < p.length; i++) {
				p[i]=Reader.nextInt();
			}
			boolean ans1=true;
			boolean ans2=true;
			int a=p[0];
			int i;
			for (i = 1; i < p.length; i++) {
				if(a+1!=p[i]) {
					break;
				}
				a=p[i];
			}
			if(i<n && p[i]!=1)
				ans1=false;
			else {
				a=1; i++;
				while(i<n) {
					if(a+1!=p[i]) {
						ans1=false;
						break;
					}
					i++;
				}
			}
			if(ans1) {
				System.out.println("YES");
				continue;
			}
			a=p[0];
			i=0;
			for (i = 1; i < p.length; i++) {
				if(a-1!=p[i]) {
					break;
				}
				a=p[i];
			}
			if(p[0]+1!=p[n-1]) {
				ans2=false;
			}
			else {
				int j=n-2;
				a=p[n-1];
				while(j>=i) {
					if(a+1!=p[j]) {
						ans2=false;
						break;
					}
					a=p[j];
					j--;
				}
			}
			if(ans2) {
				System.out.println("YES");
				continue;
			}
			System.out.println("NO");
			
		}
	}
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
