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.to_i
ary = gets.split.map(&:to_i)
cnt = 1
if N > 1
    plus_mode = 0 # -1: 減少中, 0: 未決定, 1: 増加中
    1.upto(ary.size-1) do |n|
        case plus_mode
        when -1
            if ary[n] > ary[n-1]
                cnt += 1
                plus_mode = 1
            end
        when 0
            if ary[n] > ary[n-1]
                plus_mode = 1
            elsif ary[n] < ary[n-1]
                plus_mode = -1
            end
        when 1
            if ary[n] < ary[n-1]
                cnt += 1
                plus_mode = 0
            end
        end
    end
end
puts cnt