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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn

object Main extends App {
  val n  = StdIn.readLine().toInt
  val p :Array[Int] = StdIn.readLine().split(" ").map(_.toInt)

  def solve(n: Int, p: Array[Int]): Int = {
    var v = 0
      (0 to (n - 3)).foreach {i =>

        if (p(i) < p(i + 1) && p(i + 1) < p(i + 2)) v = v + 1
        else if (p(i) > p(i + 1) && p(i + 1) > p(i + 2)) v = v + 1
      }

    v
  }

  println(solve(n, p))
}