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 Python (3.4.3) (judge verdict: Accepted)

import math

N = int(input())
A_list = list(map(int, input().split()))

num_split = 1
sign = None
len_A_list = len(A_list)

for i in range(len_A_list-1):
    if sign == None:
        if A_list[i+1] - A_list[i] == 0:
            continue
        sign = (A_list[i+1] - A_list[i]) / math.fabs(A_list[i+1] - A_list[i])

    if (A_list[i+1] - A_list[i]) *  sign >= 0:
        continue

    num_split += 1
    sign = None

print(num_split)