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.InputStream;
import java.io.PrintStream;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    AnsCounter counter = new AnsCounter();
    IntStream.range(0, n).mapToObj(i -> sc.next())
      .forEach(s -> counter.add(Integer.valueOf(s)));
    pw.println(counter.count);
  }

  private static class AnsCounter {

    int count = 0;
    LinkedList<Integer> numbers = new LinkedList<>();

    void add(Integer n) {
      if (numbers.size() == 3) {
        numbers.poll();
      }
      numbers.add(n);
      if (numbers.size() == 3) {
        int elem1 = numbers.get(0);
        int elem2 = numbers.get(1);
        int elem3 = numbers.get(2);
        if (elem1 <= elem2 && elem2 < elem3) {
          count++;
        }
        if (elem3 <= elem2 && elem2 < elem1) {
          count++;
        }
      }
    }
  }
}