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 2.0.3) (judge verdict: Accepted)

(let* ((n (read))
    (p (make-array n))
    (ans 0))

    (loop for i below n do
        (setf (aref p i) (read))
    )

    (loop for i from 1 below (- n 1) do
        (let ((a (make-array 3)))
            (setf (aref a 0) (aref p (- i 1)))
            (setf (aref a 1) (aref p i))
            (setf (aref a 2) (aref p (+ i 1)))
            (setf a (sort a #'<))
            (if (= (aref p i) (aref a 1))
                (incf ans)
            )
        )
    )
    (princ ans)
)