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 search(v, A, B, flg, p, c, s):
  if flg[v-1] == 1:
    return c
#  print("v=", v, "flg=", flg, "p=", p, "cnt=", c)
  flg[v-1] = 1
  for idx in A:
    if v == A[idx]:
      c += 1
      if search(B[idx], A, B, flg, p, c, s) == 0:
        return 0
  for idx in B:
    if v == B[idx]:
      c += 1
      if search(A[idx], A, B, flg, p, c, s) == 0:
        return 0
#  for idx in A:
#    if v==A[idx] and flg[B[idx]-1] == 0:
#      return 0
#  for idx in B:
#    if v==B[idx] and flg[A[idx]-1] == 0:
#      return 0
  p.append(v)
  return c+1

str = input()
NM = list(map(int,str.split()))
print(NM)
ANS = 1
AB = []
C = []
A = []
B = []
for i in range(0,int(NM[1])):
  str = input()
  AB.append(list(map(int,str.split())))
  A.append(AB[i][0])
  B.append(AB[i][1])
#print(AB)
e = 0  # end vertex
#
# Start path finding
#
for i in range(0,int(NM[1])):  # Choose start vertex
  flg = [] # Clear the flag list
  for j in range(0,int(NM[0])):
    flg.append(0)
  c = AB[i][0]  # current vertex
  s = c   # start vertex
  p = []
#  print("A=", A, "B=", B)
  cnt = search(c, A, B, flg, p, 0, s)
  if cnt != 0:
#    print(p)
    print(cnt)
    for i in p:
      print(i)
    break