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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun readseq (num)
  (loop 
    as i 
    below num 
    collect (read)
  )
)

(defun ismonoinc (l)
  (or 
    (< (first l) (second l) (third l))
    (> (first l) (second l) (third l))
  )
)

(defun createordinaryseq (n seq)
  (loop 
    as i below (- n 2) 
    collect (ismonoinc (list (first seq) (second seq) (third seq)))
    do (setq seq (cdr seq))
  )
)
    
(let* (
    (n (read))
    (seq (readseq n))
  )
  (princ (count T (createordinaryseq n seq)))
)