Problem:
Score : 300 points

Problem Statement

You are given an array A of length N.
Your task is to divide it into several contiguous subarrays.
Here, all subarrays obtained must be sorted in either non-decreasing or non-increasing order.
At least how many subarrays do you need to divide A into?

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Each A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible number of subarrays after division of A.

Sample Input 1

6
1 2 3 2 2 1

Sample Output 1

2

One optimal solution is to divide the array into [1,2,3] and [2,2,1].

Sample Input 2

9
1 2 1 2 1 2 1 2 1

Sample Output 2

5

Sample Input 3

7
1 2 3 2 1 999999999 1000000000

Sample Output 3

3

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

#[derive(PartialEq, Debug)]
enum NumsState {
    Incr,
    Decr,
    Unknown,
}

fn main() {
    let _: i32           = read();
    let nums: Vec<i32>   = read_vec();
    let (_, _, count, _) = nums.iter().fold(
        (*nums.get(0).unwrap(), NumsState::Unknown, 1, 1),
        |tuple: (i32, NumsState, i32, i32), num| {
            let (before_num, state, count, section_len) = tuple;
            let new_state = match state {
                NumsState::Incr    => if before_num > *num { NumsState::Decr } else { NumsState::Incr },
                NumsState::Decr    => if before_num < *num { NumsState::Incr } else { NumsState::Decr },
                NumsState::Unknown => {
                    if before_num < *num {
                        NumsState::Incr
                    } else if  before_num > *num {
                        NumsState::Decr
                    } else {
                        NumsState::Unknown
                    }
                },
            };
            let new_section_len = if state == new_state {
                section_len + 1
            } else {
                match state {
                    NumsState::Unknown => section_len + 1,
                    _                  => if section_len > 1 { 1 } else { section_len + 1 },
                }
            };
            let new_count = if new_section_len == 1 { count + 1 } else { count };
            (*num, new_state, new_count, new_section_len)
        }
    );
    println!("{}", count);
}