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.lang.*;
import java.io.*;

public class TestClass {
	static FastReader sc;
	static int mod = (int) Math.pow(10, 9) + 7;
	static BufferedWriter log;

	public static void main(String[] args) throws IOException {
		log = new BufferedWriter(new OutputStreamWriter(System.out));
		sc = new FastReader();
		int t = sc.nextInt();
//		int t = 1;
		for (int i_t = 0; i_t < t; i_t++) {
			int n = sc.nextInt();
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = sc.nextInt();
			log.write(solve(a, n) + "\n");
//			log.write("Case #"+(i_t+1)+": " + ans + "\n");
		}
		log.flush();

	}

	private static String solve(int[] a, int n) {
		int i = 0;
		for (int j = 0; j < n; j++)
			if (a[j] == 1) {
				i = j;
				break;
			}
		return (left(a,n,i)||right(a,n,i))?"YES":"NO";
	}

	private static boolean left(int[] a, int n, int i) {
		int val=2;i--;
		while(i>=0)
			if(a[i--]!=val++)
				return false;
		i=n-1;
		while(val<=n)
			if(a[i--]!=val++)
				return false;
		
		return true;
	}
	
	private static boolean right(int[] a, int n, int i) {
		int val=2;i++;
		while(i<n)
			if(a[i++]!=val++)
				return false;
		i=0;
		while(val<=n)
			if(a[i++]!=val++)
				return false;
		
		return true;
	}

	private static void pL(long l) throws IOException {
		log.write(Long.toString(l) + "\n");
	}

	public static void pA(int[] a, int n) {
		try {
			for (int i = 0; i < n; i++) {
				log.write(a[i] + " ");
			}
			log.write("\n");
			log.flush();
		} catch (Exception e) {

		}
	}

	public static <T> void pA(T[] a, int n) throws IOException {
		for (int i = 0; i < n; i++) {
			log.write(a[i].toString() + "\n");
		}
		log.write("\n");
	}

	public static void pM(int[][] dp2, int n, int m) throws IOException {
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				log.write(dp2[i][j] + " ");
			}
			log.write("\n");
		}
	}

	public static void pM(long[][] dp2, int n, int m) throws IOException {
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				log.write(dp2[i][j] + " ");
			}
			log.write("\n");
		}
	}

}

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());
	}

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