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: Runtime Error)

N = int(input())
a = list(map(int, input().split(" ")))


l = [[] for i in range(N)]
c = 0

s = 0
t = a[0]

for i in a[1:]:
	if t > i:
		l[s].append((c))
		s = c+1
	c += 1
	t = i
else:
	l[s].append((c))

c = 0

s = 0
t = a[0]

for i in a[1:]:
	if t < i:
		l[s].append((c))
		s = c+1
	c += 1
	t = i
else:
	l[s].append((c))

l[0] = max(l[0])
for i in range(1,N):
	if i!=N-1:
		l[i+1].append(-1)
		l[i] = max(l[i-1],max(l[i]),max(l[i+1]))
	else:
		l[i] = max(l[i-1],max(l[i]))


now = 0
res = 0

while now<N-1:
	now = l[now]	
	res+=1

print(res)