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)

use std::io;


fn main() {
    let mut n = String::new();
    let mut p = String::new();

    io::stdin().read_line(&mut n).ok();
    io::stdin().read_line(&mut p).ok();

    n = n.trim_right().to_owned();
    p = p.trim_right().to_owned();

    let mut n: usize = n.parse().unwrap();
    let mut i = p.split_whitespace();
    let mut p: Vec<i32> = Vec::new();

    for _ in 0..n {
        p.push(i.next().unwrap().parse().unwrap());

    };

    let mut ans = 0;

    for j in 1..n-1 {
        let mut q = [ p[j-1], p[j], p[j + 1]];
        q.sort();
        if p[j] == q[1] {
            ans += 1;
        };
    };
    println!("{}", ans);
}