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)

(let ((n (read))
      (a (make-array 0 :element-type 'integer
                       :adjustable t
                       :fill-pointer 0))
      (ans 0))
     (dotimes (i n)
       (vector-push-extend (read) a))
     (loop for i from 1 upto (- n 2)
           do (if (or (and (< (aref a (1- i)) (aref a i)) (< (aref a i) (aref a (1+ i)))) (and (> (aref a (1- i)) (aref a i)) (> (aref a i) (aref a (1+ i))))) (incf ans)))
     (princ ans))