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)

import numpy as np
N = int(input())
As = input().split()
for i in range(N):
    As[i] = int(As[i])
As = np.array(As)


def get_sign(x):
    if x>0:
        return +1
    elif x<0:
        return -1
    else:
        return 0

ans = 1
a0 = None
a1 = None
for a in As:
    if a0 is None:
        a0 = a
    elif a1 is None:
        a1 = a
    else:
        if (get_sign(a-a1)==get_sign(a1-a0))|(get_sign(a-a1)==0):
            a0 = a1
            a1 = a
        else:
            ans += 1
            a0 = a
            a1 = None
print(ans)