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 input = String::new();
    io::stdin().read_line(&mut input).ok();
    let n: usize = input.trim().parse().unwrap();

    let mut input = String::new();
    io::stdin().read_line(&mut input).ok();
    let mut v: Vec<isize> = Vec::new();
    for z in input.trim().split_whitespace() {
        v.push(z.parse().unwrap());
    }

    let mut cn = 0;

    for z in 0..n - 2 {
        if (v[z] < v[z + 1] && v[z + 1] < v[z + 2]) || (v[z] > v[z + 1] && v[z + 1] > v[z + 2]) {
            cn += 1;
        }
    }

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