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 Data.List (group)

solve [_] cnt upper = cnt
solve [x0,x1] cnt upper
  | x0 < x1 && upper = cnt
  | x0 > x1 && not upper = cnt
  | otherwise = cnt+1
solve (x0:x1:x2:xs) cnt upper
  | x0 < x1 && upper = solve (x1:x2:xs) cnt upper
  | x0 > x1 && not upper = solve (x1:x2:xs) cnt upper
  | otherwise = solve (x2:xs) (cnt+1) (x1<x2)

main = do
  n <- read <$> getLine :: IO Int
  as <- map head.group.map read.words <$> getLine :: IO [Int]
  print $  solve as 1 (head as<(head.tail) as)