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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;


public class Main {
	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
	

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

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
    public static long mod = (long) (1e9+7);
    public final static int MAX = (int)1e5;
  // static Scanner sc = new Scanner(System.in);
   static List<Integer>[] edge;
	public static void main(String[] args) {
	   
	 FastReader sc = new FastReader();
	   int t = sc.nextInt();
	   while(t-->0) {
		   int n = sc.nextInt();
		   int[] a = new int[n];
		   for(int i=0;i<n;++i) a[i] = sc.nextInt();
		   int idx = -1 ;
			for(int i = 0 ; i < n ; i++){
				if(a[i] == 1) {
					idx = i ; break ;
				}
			}
		   if(clc(a,idx,n) || anti(a,idx,n)) out.println("YES");
		   else out.println("NO");
	   }
	   out.close();
	}
	 static boolean clc(int[] a , int idx , int n){
		for(int i = 1 ; i < n ; i++ ){
			if(a[(idx+i)%n] != i+1) return false ;
		}
		return true ;
	}

      static boolean anti(int[] a , int idx , int n){
		for(int i = 1 ; i < n ; i++){
			if(a[(idx-i+n)%n] != i+1) return false ;
		}
		return true ;
	}
}