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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
  let n: usize = {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().unwrap()
  };
  let p: Vec<i32> = {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.split_whitespace()
      .map(|x| x.parse().unwrap())
      .collect()
  };
  let cnt = (1..n-1).filter(|&i| (p[i-1] < p[i] && p[i] < p[i+1]) || (p[i-1] > p[i] && p[i] > p[i+1])).count();
  println!("{}", cnt);
}