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: Accepted)

import Control.Applicative ((<$>), (<*>))
import Control.Monad
import Data.List

main :: IO ()
main = do
  solve <$> getl read <*> getl (map read . words) >>= print

solve :: Int -> [Int] -> Int
solve n xs = fst $ foldl f (1,H) $ map tr $ zip (tail xs) xs
  where
    tr (x, y)
      | x == y = H
      | x > y = D
      | otherwise = U
    f (c, prs) cts = case (prs, cts) of
      (H, H) -> (c, H)
      (H, U) -> (c, U)
      (H, D) -> (c, D)
      (U, H) -> (c, U)
      (U, U) -> (c, U)
      (U, D) -> (c+1, H)
      (D, H) -> (c, D)
      (D, U) -> (c+1, H)
      (D, D) -> (c, D)

data State = U | D | H

getl :: (String -> a) -> IO a
getl f = f <$> getLine