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)

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

ans = 1

#state0は未定、1は広義単調増加、2は広義単調減少
state = 0
m = A[0]

i = 1
while i <= N-1:
    if m < A[i]:
        if state == 0:
            state = 1
        elif state == 2:
            ans += 1
            state = 0
    elif m > A[i]:
        if state == 0:
            state = 2
        elif state == 1:
            ans += 1
            state = 0
    m = A[i]
    i += 1

print(ans)