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 (1.15.1) (judge verdict: Accepted)

fn get_input() -> String {
    let mut word = String::new();
    std::io::stdin().read_line(&mut word).ok();
    return word.trim().to_string();
}

fn main() {
    let n:usize = get_input().parse().unwrap();

    let mut p:Vec<u32> = Vec::with_capacity(n);

    for i in get_input().split_whitespace() {
        p.push(i.parse().unwrap());
    }

    let mut ans = 0;
    for i in 1..p.len()-1 {
        let mut a = [p[i-1], p[i], p[i+1]];
        a.sort();
        if a[1] == p[i] {
            ans += 1;
        }
    }
    println!("{}", ans);

}