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 OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let a = Array.init n (fun _ -> Scanf.scanf " %d" (fun a -> a)) in

    let rec loop i mode acc =
        if i = n then acc else
            match mode with
            | 0 -> if a.(i) < a.(i - 1) then loop (i + 1) (-1) acc else
                   if a.(i) > a.(i - 1) then loop (i + 1) (+1) acc else
                                             loop (i + 1) mode acc
            | 1 -> if a.(i) > a.(i - 1) then loop (i + 1) mode acc else
                                             loop (i + 1) 0 (acc + 1)
            | _ -> if a.(i) < a.(i - 1) then loop (i + 1) mode acc else
                                             loop (i + 1) 0 (acc + 1)
    in
    loop 1 0 1 |> Printf.printf "%d\n"
)