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.math._

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt
  val p = List.fill(n)(sc.nextInt)

  val ans = p.foldLeft((0, (None, None, None)): (Int, (Option[Int], Option[Int], Option[Int])))((acc, v) => {
      val current = (acc._2._2, acc._2._3, Some(v))
      current match {
        case (Some(v1), Some(v2), Some(v3)) =>
          if ((v1 < v2 && v2 < v3) || (v3 < v2 && v2 < v1)) (acc._1 + 1, current)
          else (acc._1, current)
        case _ =>
          (0, current)
      }
    }
  )._1

  println(ans)

  ///////////////////////////////////////////

  def bigIterator(start: BigInt, end: BigInt, step: BigInt = 1) =
    Iterator.iterate(start)(_ + step).takeWhile(_ <= end)

  def lcm(a :Int, b :Int): Int =
    a / gcd(a, b) * b

  def lcm(a :Long, b :Long): Long =
    a / gcd(a, b) * b

  def gcd(a: Int, b: Int): Int =
    if (b == 0) a else gcd(b, a % b)

  def gcd(a: Long, b: Long): Long =
    if (b == 0) a else gcd(b, a % b)
}