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 OCaml (4.10.0) (judge verdict: Accepted)

let () = Scanf.scanf "%d" @@ fun n ->
  let ps = Array.init n @@ fun _ -> Scanf.scanf " %d" Fun.id in
  let ids = Array.init (n - 2) @@ fun i -> i + 1 in
  let check acm id = if (ps.(id - 1) < ps.(id) && ps.(id) < ps.(id + 1)) || (ps.(id - 1) > ps.(id) && ps.(id) > ps.(id + 1)) 
                      then acm + 1 else acm in
  let ans = Array.fold_left check 0 ids in
  Printf.printf "%d\n" ans