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: Wrong Answer)

n, *lst = map(int, open(0).read().split())
if n < 3:
  print(0)
  quit()
group = 0
start = (lst[1] >= lst[0])
for i in range(2, n - 1):
  if (lst[i] >= lst[i - 1]) != start:
    start = (lst[i + 1] >= lst[i])
    group += 1
if (lst[-1] >= lst[-2]) != start:
  group += 1
if group != 0:
  group += 1
print(group)