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=int(input())
a=list(map(int,input().split()))
flag=[False for i in range(n)]

count=0
for i in range(n-2):
    if i%2==0:
        if (a[i+1]-a[i])*(a[i+2]-a[i+1])<0: count+=1; flag[i]=True
    else:
        if not flag[i-1] and (a[i+1]-a[i])*(a[i+2]-a[i+1])<0: count+=1

ans=count+1
print(ans)