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())
a=list(map(int,input().split()))
b=a.copy()
b.insert(0,0)

#連続する重複を除外
arr=np.array(b)
diff=np.diff(arr)
arr2=np.array(a)
aa=arr2[np.nonzero(diff)]
print(diff,aa)

aaa=aa.tolist()
point=[]
cnt=1
print(aaa)
if len(aaa)<=2:
    print(1)
else:
    for i in range(len(aaa)-2):
        if (aaa[i+1]-aaa[i])*(aaa[i+2]-aaa[i+1])<0:
            cnt+=1
            point.append(i)
    
    if len(point)>1:
        for i in range(1,len(point)):
            if point[i]-1==point[i-1]:
                point[i]-=1
                cnt-=1
    print(cnt)