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.Arrow

main = do
  n <- getLine
  as <- map read . words <$> getLine :: IO [Int]

  print $ length $ solve as

  where
    solve [] = []
    solve xs = if length a >= length d then a : solve as else d : solve ds
      where
        (a,as) = aux xs 1
        (d,ds) = aux xs (-1)

    aux (x:[]) _ = ([x],[])
    aux (x:y:xs) 1 = if x<=y then first (x:) (aux (y:xs) 1) else ([x], y:xs)
    aux (x:y:xs) (-1) = if x>=y then first (x:) (aux (y:xs) (-1)) else ([x], y:xs)