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 7.10.3) (judge verdict: Wrong Answer)

import qualified Data.ByteString.Char8 as B
import Data.List

main = do
  _ <- getLine
  as <- map (maybe undefined fst . B.readInt) . B.words <$> B.getLine
  print (sarray as)

sarray as
  | null ds = 1
  | head ds < 0 = length (cut True as)
  | otherwise = length (cut False as)
  where
    ds = filter (/= 0) $ zipWith (-) (tail as) as

cut _ [] = []
cut False xs = () : cut True (dropWhileBy (<=) xs)
cut True xs = () : cut False (dropWhileBy (>=) xs)

takeWhileBy _ [] = []
takeWhileBy _ [x] = [x]
takeWhileBy op (x1:xxs@(x2:_))
  | op x1 x2 = x1 : takeWhileBy op xxs
  | otherwise = [x1]

dropWhileBy _ [] = []
dropWhileBy _ [x] = []
dropWhileBy op (x1:xxs@(x2:_))
  | op x1 x2 = dropWhileBy op xxs
  | otherwise = xxs