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)

def inpl(): return [int(i) for i in input().split()]
def next(v):
    for i in edge[v]:
        if visited[i]:
            continue
        visited[i] = True
        return i
    return -1

from collections import defaultdict
edge = defaultdict(lambda: [])
N, M = inpl()
visited = [False for _ in range(N+1)]
visited[1] = True
for _ in range(M):
    A,B = inpl()
    edge[A].append(B)
    edge[B].append(A)
v = 1
nv = 1
path = [1]
while nv >= 0:
    nv = next(v)
    path.append(nv)
    v = nv
path.pop()
path = list(reversed(path))
v = 1
nv = 1
while nv >= 0:
    nv = next(v)
    path.append(nv)
    v = nv
path.pop()
print(len(path))
print(*path)