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)

(defmacro defsolver (name vars &body body)
  `(defun ,name ()
     (let (,@(mapcar #'list
            vars
            (mapcar (constantly '(read))
                vars)))
       ,@body)))

(defsolver solution-b (n)
  (let ((l (loop for i below n collect (read))))
    (princ
     (loop for i from 1 below (- n 1)
	count (let ((ll
		     (sort (list (nth (1- i) l)
				 (nth i l)
				 (nth (1+ i) l))
			   #'<)))
		(= (nth i l)
		   (nth 1 ll)))))))

(solution-b)