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 OCaml (4.02.3) (judge verdict: Accepted)

let rec remove value lst =
	let rec remove_sub rel value lst =
		match lst with
		| []      -> []
		| x :: xs ->
			if rel value x then remove_sub rel x xs
			else x :: xs
	in
	match lst with
	| []      -> []
	| x :: xs ->
		if value < x then remove_sub (<=) x xs
		else if value > x then remove_sub (>=) x xs
		else remove x xs

let rec solve count lst =
	match lst with
	| []      -> count
	| x :: xs -> solve (count + 1) (remove x xs)

let () =
	let n = read_int () in
	let a =
		read_line ()
		|> Str.split (Str.regexp " ")
		|> List.map int_of_string
	in
	solve 0 a
	|> print_int
	|> print_newline