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 main() {
    let n ={
        let mut inputline = String::new();
        std::io::stdin().read_line(&mut inputline).ok();
        inputline.trim().parse::<usize>().unwrap()
    };
    let p:Vec<usize> = {
        let mut inputline = String::new();
        std::io::stdin().read_line(&mut inputline).ok();
        inputline.split_whitespace().map(|x|x.parse::<usize>().unwrap()).collect()
    };
    let count ={ 
        let mut count = 0;
        for i in 1..n-1{
            if (p[i-1]<p[i] && p[i]<p[i+1]) || (p[i+1]<p[i] && p[i]<p[i-1]){
                count = count +1;
            }
        }
        count
    };
    println!("{}",count);
}