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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int,x)
parseMap(x::Array{SubString{String}, 1}) = map(parseInt, x)

function main()
  n = parseInt(readline())
  p = map(parseInt,split(readline()))
  k=0
  for i=2:(n-1)
    if p[i-1] >= p[i] >= p[i+1]
      if p[i+1] >= p[i] >= p[i-1]
        k = k+1
      end
    end
  end
  println(k)
end

main()