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 Ruby (2.3.3) (judge verdict: Accepted)

def main(argv)
  n = gets.chomp.to_i
  p = gets.chomp.split(' ').map(&:to_i)
  
  counter = 0
  (n - 2).times do |i|
    f1 = p[i + 0] < p[i + 1] && p[i + 1] < p[i + 2]
    f2 = p[i + 0] > p[i + 1] && p[i + 1] > p[i + 2]
    if f1 || f2 then
      counter += 1
    end
  end
  puts counter.to_s
end

if self.to_s == 'main' then
  main(ARGV)
end