Problem:
Score : 200 points

Problem Statement

We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.

Print the number of elements p_i (1 < i < n) that satisfy the following condition:

p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

Constraints

All values in input are integers.

3 \leq n \leq 20

p is a permutation of {1,\ 2,\ ...,\ n}.

Input

Input is given from Standard Input in the following format:

n
p_1 p_2 ... p_n

Output

Print the number of elements p_i (1 < i < n) that satisfy the condition.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

2

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StringReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main  implements Runnable {

    public static void main(String[] args) {

        new Thread(null, new Main(), "", 16 * 1024 * 1024).start();

    }

    public void run() {
    	FastScanner sc = new FastScanner(System.in);
		//long n = Long.parseLong(sc.next());
    	//int[] ar = new int[3];
    	//ar[0]=Integer.parseInt(sc.next());
    	//ar[1]=Integer.parseInt(sc.next());
    	//ar[2]=Integer.parseInt(sc.next());
    	//Arrays.parallelSort(ar);
		int n = Integer.parseInt(sc.next());
		//int k = Integer.parseInt(sc.next());
		//int l = Integer.parseInt(sc.next());
		//long a = Long.parseLong(sc.next());
		//String s = sc.next();
		//int k = Integer.parseInt(sc.next());
		//int m = Integer.parseInt(sc.next());
		//int x2000 = Integer.parseInt(sc.next());
		//int t = Integer.parseInt(sc.next());
		//int k = 0;
		//int k = Integer.parseInt(sc.next());
		//String str = sc.next();
		//char c[] = str.toCharArray();
		//char a[][] = new char[n];
		//int atmp[] = new int[h];
		//int max= 0;
		//int blackar[][] = new int[h*w][2];
		//int p=0;
		//ArrayList<Integer> lists = new ArrayList<Integer>();
		//lists = new ArrayList;
		PrintWriter out = new PrintWriter(System.out);
		int[] a = new int[n];
		int ans = 0;
		for(int i = 0; i< n; i++)
		{
			a[i] = Integer.parseInt(sc.next());
			if(i>=2)
			{
				if(a[i-2] < a[i-1] && a[i-1] < a[i-0])
				{
					ans++;
				}
				else if (a[i-2] > a[i-1] && a[i-1] > a[i-0])
				{
					ans++;
				}
			}
		}

			out.println(ans);


		out.flush();
	}

    static class FastScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;
        public FastScanner(String in) {
        	StringReader sr = new StringReader(in);
            reader = new BufferedReader(new BufferedReader(sr));
            tokenizer = null;
        }
        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

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

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

            return tokenizer.nextToken("\n");
        }

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

        public long nextInt() {
            return Integer.parseInt(next());
        }

    }


}