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)

object Main{
  def main(args: Array[String]){
      val input=io.Source.stdin.getLines().mkString("\n")
      println(solve(input).toString.trim());
  }
  def solve(input:String):Int ={
    val g = input.split("\n")(1).split(" ").map(_ .toInt)
    var ret = 0
    for( i <- 1 until g.size-1){
    	if( ( g(i-1) < g(i) && g(i) <= g(i+1) )|| ( g(i-1) >= g(i) && g(i) > g(i+1) ) )
        {
         ret +=1
        }
    }
    ret
  }
}