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 splitat (c line)
  (labels ((rec (line acc)
				(let ((pos (position-if (lambda(cc) (char= c cc)) line)))
				  (if pos
					  (rec (subseq line (1+ pos)) (cons (subseq line 0 pos) acc))
					(nreverse (cons line acc))))))
	(rec line nil)))
(defun f (ns line)
  (let* ((n (parse-integer ns))
		 (arr (map 'vector (lambda(a) (parse-integer a)) (splitat #\space line))))
	(labels ((rec (i acc)
				  (if (< i (- n 2))
					(progn
					  (let ((a0 (elt arr i))
							(a1 (elt arr (1+ i)))
							(a2 (elt arr (+ i 2))))
						(rec (1+ i) (if (or (and (<= a0 a1) (<= a1 a2))
											(and (>= a0 a1) (>= a1 a2))
											)(1+ acc) acc))))
					acc)))
	  (format t "~A" (rec 0 0)))))

(let (
	  (line0 (read-line nil nil))
	  (line1 (read-line nil nil))
	  )
  (f line0 line1))