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::str::FromStr;

#[allow(unused_macros)]
macro_rules! scan {
  ($e:expr; $t:ty) => {
    $e.get::<$t>()
  };
  ($e:expr; $($t:ty), *) => {
    ($($e.get::<$t>(),)*)
  };
  ($e:expr => $i:expr; $t:ty) => {
    (0..$i).map(|_| $e.get::<$t>()).collect::<Vec<$t>>()
  };
  ($e:expr => $row:expr, $col:expr; $t:ty) => {
    (0..$i).map(|_| scan!($e => $col; $t)).collect::<Vec<$t>>()
  }
}

struct Scanner<R: Read> {
  reader: R
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
  fn new(reader: R) -> Scanner<R> {
    Scanner { reader: reader }
  }
  fn safe_get<T: FromStr>(&mut self) -> Option<T> {
    let token = self.reader.by_ref().bytes().map(|c| c.unwrap() as char)
      .skip_while(|c| c.is_whitespace())
      .take_while(|c| !c.is_whitespace())
      .collect::<String>();
    if token.is_empty() { None } else { token.parse().ok() }
  }
  fn get<T: FromStr>(&mut self) -> T {
    if let Some(v) = self.safe_get() { v } else {
      writeln!(stderr(), "Terminated with EOF").unwrap();
      std::process::exit(0);
    }
  }
}

trait Writable {
  fn write(&self, sep: &'static str) -> String;
}

impl<T: ToString> Writable for Vec<T> {
  fn write(&self, sep: &'static str) -> String {
    self.iter().map(|e| e.to_string()).collect::<Vec<String>>().join(sep)
  }
}

macro_rules! max {
  ($v0:expr, $v1:expr) => { max($v0, $v1) };
  ($v0:expr, $v1:expr, $($v:expr),*) => { max!(max($v0, $v1), $($v), *) }
}

macro_rules! min {
  ($v0:expr, $v1:expr) => { min($v0, $v1) };
  ($v0:expr, $v1:expr, $($v:expr),*) => { min!(min($v0, $v1), $($v), *) }
}


fn main() {
  let cin = stdin();
  let cin = cin.lock();
  let mut sc = Scanner::new(cin);
  let n = scan!(sc; i32);
  let p = scan!(sc => n; i32);

  let mut ans = 0;
  for i in 1..(p.len() - 1) {
    if max!(p[i - 1], p[i], p[i + 1]) != p[i] && min!(p[i - 1], p[i], p[i + 1]) != p[i] {
      ans += 1
    }
  }

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

fn max<T: Ord>(a: T, b: T) -> T { if a > b { a } else { b } }
fn min<T: Ord>(a: T, b: T) -> T { if a < b { a } else { b } }