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::stdin;

fn main() {
    let mut n = String::new();
    stdin().read_line(&mut n).unwrap();
    let n: usize = n.trim().parse().unwrap();

    let mut ps = String::new();
    stdin().read_line(&mut ps).unwrap();
    let ps: Vec<usize> = ps.trim().split_whitespace().flat_map(str::parse).collect();

    let mut res = 0;
    for i in 1..n-1 {
        let mut a: Vec<_> = ps.clone().into_iter().skip(i-1).take(3).collect();
        a.sort();
        if a[1] == ps[i] {
            res += 1;
        }
    }
    println!("{}", res);
}