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.*;
import java.util.*;
import java.lang.*;
import java.math.*;

public class A {
	public void run() throws Exception {
		FastScanner sc = new FastScanner();
		
		int q = sc.nextInt();
		for (int i = 0; i<q; i++) {
			int n = sc.nextInt();//System.out.println(n);
			
			int[] arr = new int[n+1];
			for (int j = 0; j<n; j++) {
				arr[j] = sc.nextInt();
			}if (n<4) {
				System.out.println("YES");
				continue;
			}
			
			arr[n] = arr[0];
			int diff = 0;
			if (arr[1]-arr[0] == n-1) diff = arr[2]-arr[1];
			else if (arr[1] - arr[0] == -1) diff = -1;
			else diff = 1;
			
			boolean ok = true;
			int over = 0;
			for (int j = 0; j<n; j++) {
				if(Math.abs(arr[j+1]-arr[j]) == n-1) {
					over++; continue;
				}
				else if (arr[j+1]-arr[j] != diff) {
					ok = false;
					break;
				}//System.out.println(diff);
			}
			//System.out.println(ok + " " + over);
			if (!ok || over>1) System.out.println("NO");
			else System.out.println("YES");
		}
		
	}
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 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());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

	}
	public static void main (String[] args) throws Exception {
		new A().run();
	}
}