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

public class ProblemA {
	public static void main(String[] args) throws IOException {
		InputStream in = System.in;
		InputReader scan = new InputReader(in);
		int q = scan.nextInt();
		for(int t=0;t<q;t++) {
			int n = scan.nextInt();
			int[] pos = new int[n];
			for(int i=0;i<n;i++) {
				int elem = scan.nextInt();
				pos[elem-1] = i;
			}
			boolean flag = false;
			if(n==1) flag = true;
			//clockwise
			if(!flag) {
				for(int i=1;i<n;i++) {
					if(pos[i]==getModIndex(pos[i-1],n,1)) {
						if(i==n-1) flag = true;
					} else {
						break;
					}
				}
			}
			//anti-clockwise
			if(!flag) {
				for(int i=1;i<n;i++) {
					if(pos[i]==getModIndex(pos[i-1],n,-1)) {
						if(i==n-1) flag = true;
					} else {
						break;
					}
				}
			}
			if(flag) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
		}
	}
	
	static int getModIndex(int currIndex,int size,int offset) {
		return (currIndex+offset+size)%size;
	}
	
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}
