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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets()
a_str = gets()
a = a_str.split(" ")

n_num = n.to_i
stop = 0
count = 0
times = 1
while stop == 0
	b1 = a[count]
	b2 = a[count +1]
	b3 = a[count + 2]
	c1 = b1.to_i
	c2 = b2.to_i
	c3 = b3.to_i
	if count + 2 > n_num -1
		if c1 < c2
			c3 = 1000000000
		elsif c1 > c2
			c3 = 0
		end
	end
	if c1 < c2 && c2 > c3
		times = times + 1
		count = count + 2
	elsif c1 > c2 && c2 < c3
		times = times + 1
		count = count + 2
	else
		count = count + 1
	end
	if count == n_num
		stop = 1
	end
end

puts(times)