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.Monad
import Data.List

main :: IO ()
main = do
  n <- readLn :: IO Int
  as <- map (read :: String -> Int) . words <$> getLine
  print $ solve as

solve :: [Int] -> Int
solve as = go as' (if length as' /= 1
                   then (head y <= head (head ys))
                   else True)
  where
    as'@(y:ys) = group as
    go :: [[Int]] -> Bool -> Int
    go [] _ = 0
    go [x] _ = 1
    go (x:xs@(z:zs)) b
      | head x <= head z , b = go xs b 
      | head x >= head z , not b = go xs b
      | otherwise = if (not.null) zs
                    then 1 + go zs (head z <= head (head zs))
                    else 1 + go xs b