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 BS
import Data.Maybe (fromJust)
import Data.List

solve :: [Int] -> [Int]
solve [_] = []
solve (x1:x2:xs) = xx : solve (x2:xs)
  where
    xx | x1 < x2  = 1
       | x1 > x2  = 2
       | x1 == x2 = 0

main :: IO ()
main = do
    _ <- getLine
    a <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    let ga = map head . group . filter (/=0) $ solve a
        a1 = length $ filter (==1) ga
        a2 = length $ filter (==2) ga
    print $ 1 + max a1 a2