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 input() -> i32 {
    let s = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    };
    let mut integers = s.split_whitespace();
    let integer: i32 = integers.next().unwrap().parse().unwrap();
    integer
}
fn input_char() -> char {
    let s = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    };
    let ch: char = {
        let mut tmp: char = 'a';
        for c in s.chars() {
            tmp = c
        }
        tmp
    };
    ch
}

fn main() {
    let n:i32 = input();
    let p: Vec<i32> = {
        let s = {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            s.trim_right().to_owned()
        };
        let integers: Vec<&str> = s.split_whitespace().collect();
        let mut vector = Vec::new();
        let mut tmp: i32;
        for element in integers {
            tmp = element.parse().unwrap();
            vector.push(tmp);
        }
        vector
    };
    // dbg!(p);
    
    let mut can: bool;
    let mut cnt = 0;
    let mut a: i32;
    let mut b: i32;
    let mut c: i32;
    
    for i in 0..(n-2) as usize {
        // dbg!(i);
        can = false;
        a = p[i];
        b = p[i+1];
        c = p[i+2];
        if a < b && b <= c {
            can = true;
        }
        if c < b && b <= a {
            can = true;
        }
        if can {
            cnt += 1;
        }
    }

    println!("{}", cnt);
}