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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Char
import Data.List

main = do
  getLine
  li <- BS.getLine
  let as = unfoldr (BS.readInt . BS.dropWhile isSpace) li
  let ans = compute as
  print ans

compute :: [Int] -> Int
compute (a:as) = ans where (ans,_,_) = foldl step (1,EQ,a) as

-- カウント、上昇中/下降中/不明、前の値
type Acc = (Int,Ordering,Int)
step :: Acc -> Int -> Acc
step (n,o,z) a = case (o,compare z a) of
  (EQ, o') -> (n, o', a)
  (LT, GT) -> (succ n, EQ, a)
  (GT, LT) -> (succ n, EQ, a)
  _        -> (n, o, a)