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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N = int(input())
Alist = list(map(int, input().split()))
if N < 3:
    print(1)
else:
    ans = 1
    last = Alist[0]
    new_a = [last]
    for i in range(N):
        now = Alist[i]
        if now != last:
            new_a.append(now)
        last = now
    now = "up" if new_a[0] < new_a[1] else "down"
    for i in range(1, len(new_a)):
        if new_a[i - 1] == new_a[i]:
            continue
        elif new_a[i - 1] < new_a[i]:
            if now == "down":
                now = "up"
                ans += 1
        elif new_a[i - 1] > new_a[i]:
            if now == "up":
                now = "down"
        # print(i, now, ans)
    print(ans + 1)