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 (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        n: usize,
        a_s: [usize; n],
    }
    #[derive(Clone, Copy)]
    enum State {
        Unknown,
        EqualOrMore,
        EqualOrLess,
    }
    use State::*;
    let mut state = Unknown;
    let mut count = 1usize;
    for w in a_s.windows(2) {
        match (state, w[0].cmp(&w[1])) {
            (Unknown, std::cmp::Ordering::Equal) => {}
            (Unknown, std::cmp::Ordering::Greater) => {
                state = EqualOrMore;
            }
            (Unknown, std::cmp::Ordering::Less) => {
                state = EqualOrLess;
            }
            (EqualOrMore, std::cmp::Ordering::Equal) => {}
            (EqualOrMore, std::cmp::Ordering::Greater) => {}
            (EqualOrMore, std::cmp::Ordering::Less) => {
                count += 1;
                state = Unknown;
            }
            (EqualOrLess, std::cmp::Ordering::Equal) => {}
            (EqualOrLess, std::cmp::Ordering::Greater) => {
                count += 1;
                state = Unknown;
            }
            (EqualOrLess, std::cmp::Ordering::Less) => {}
        }
    }
    println!("{}", count);
}