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;
use std::cmp::min;

fn main() {
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let n = buf.trim().parse::<u32>().ok().unwrap();
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let iter = buf.split_whitespace();
	let mut p = Vec::new();
	for i in iter {
		p.push(i.parse::<u32>().ok().unwrap());
	}
	let mut cnt = 0;
	for i in 1..(n-1) as usize {
		if min(p[i], p[i-1]) == p[i] && min(p[i], p[i+1]) == p[i+1] {
			cnt += 1;
		}else if min(p[i], p[i-1]) == p[i-1] && min(p[i], p[i+1]) == p[i] {
			cnt += 1;
		}
	}
	println!("{}", cnt);
}