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 Debug.Trace (traceShow)

data State = NoneDecreasing | NoneIncreasing | Unknown deriving (Eq, Show)

main = do
    n <- getLine
    xs <- map read . words <$> getLine
    print $ solve xs

solve :: [Int] -> Int
solve xs = length $ foldr fn [] xs
    where fn x [] = ([x], Unknown):[]
          fn x whole@((c, state):ys) | state == NoneDecreasing = if (isNoneDecreasing x c)
                                                                 then (x:c, state):ys
                                                                 else ([x], Unknown):whole
                                     | state == NoneIncreasing = if (isNoneDecreasing x c)
                                                                 then (x:c, state):ys
                                                                 else ([x], Unknown):whole
                                     | otherwise               = if (isNoneDecreasing x c) && (isNoneIncreasing x c)
                                                                 then (x:c, Unknown):ys
                                                                 else if (isNoneDecreasing x c)
                                                                      then (x:c, NoneDecreasing):ys
                                                                      else (x:c, NoneIncreasing):ys
isNoneIncreasing :: Ord a => a -> [a] -> Bool
isNoneIncreasing x (y:_) = not (x > y)
isNoneDecreasing :: Ord a => a -> [a] -> Bool
isNoneDecreasing x (y:_) = not (x < y)