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 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 = search 0 xs
  where
    cp x y z
      | x < y && y > z = True
      | x > y && y < z = True
      | otherwise = False
    search cnt (x:y:z:zs)
      | cp x y z = search (cnt+1) (z:zs)
      | otherwise = search cnt (y:z:zs)
    search cnt _ = cnt + 1

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