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.io.PrintWriter;
import java.util.*;
import java.math.*;
public class code {
	static int dp[][];
	static boolean visited[];
	static int ans = 0;
	public static void main(String[] args)throws IOException {
		FastReader sc = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int arr[] = new int[n];
			int ind = 0;
			for (int i = 0; i < n; i++) {
				arr[i] = sc.nextInt();
				if (arr[i] == 1)
					ind = i;

			}
			boolean flg = true;
			int tmp = 1;
			int f = 0;
			for (int i = ind; i < n; i++) {
				if (arr[i] == tmp) {
					tmp++;
					continue;
				} else {
					flg = false;
					break;
				}
			}
			if (flg) {
				System.out.println("YES");
				continue;
			}
			for (int i = 0; i < ind; i++) {
				if (arr[i] == tmp) {
					tmp++;
					continue;
				} else {
					flg = false;
					break;
				}

			}
			if (flg)
				System.out.println("YES");
			else {
				tmp = 1;
				flg = true;
				for (int i = ind; i >= 0; i--) {
					if (arr[i] == tmp) {
						tmp++;
						continue;
					} else {
						flg = false;
						break;
					}
				}
			}
			if (!flg) {
				System.out.println("NO");
				continue;
			}
			for (int i = n - 1; i > ind; i--) {
				if (arr[i] == tmp) {
					tmp++;
					continue;
				} else {
					flg = false;
					break;
				}
			}
			if (flg)
				System.out.println("YES");
			else
				System.out.println("NO");


		}

	}


}






class FastReader {
	BufferedReader br;
	StringTokenizer st;

	public FastReader() {
		br = new BufferedReader(new
		                        InputStreamReader(System.in));
	}

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException  e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	int nextInt() {
		return Integer.parseInt(next());
	}

	long nextLong() {
		return Long.parseLong(next());
	}

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

	String nextLine() {
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}
}