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)

main = do
  _ <- getLine
  as <- map read . words <$> getLine
  putStr . show . f $ as
 
f :: [Integer] -> Integer
f [] = 0
f [x] = 1
f [x, y] = 1
f [x, y, z]
  | x <= y && y <= z = 1
  | x >= y && y >= z = 1
  | otherwise = 2
f (x:y:z:ws)
  | x <= y && y <= z = f (y:z:ws)
  | x >= y && y >= z = f (y:z:ws)
  | otherwise = 1 + f (y:z:ws)