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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var
  i,j,a1,a2,n,r:integer;
  a:array[1..100005] of integer;
begin
  r:=0;
  read(n);
  for i:=1 to n do read(a[i]);
  while j<=n do
  begin
    r:=r+1;
    a1:=a[j];
    j:=j+1;
    while (a[j]=a1) and (j<=n) do j:=j+1;
    a2:=a[j];
    j:=j+1;
    while ((a1-a2) * (a[j-1]-a[j]) >= 0) and (j<=n) do j:=j+1;
  end;
  writeln(r);
end.