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 => in}

object Main extends App {
  val n = in.readInt
  val p = in.readLine.split(" ").map(_.toInt)

  val table = Array.ofDim[Int](n+1)
  for(i <- 0 until n - 2) {
    val v = Seq(p(i), p(i+1), p(i+2)).sorted
    if(v(1) == p(i+1)) {
      table(p(i+1)) += 1
    }
  }

  val ans = table.count(_ > 0)
  println(ans)
}