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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i=0;i<(n);i++)
#define REP2(i,a,b) for(int i=(a);i<(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define INF 2e9
typedef long long ll;

int main()
{
  int n;
  cin>>n;
  vector<int> a(n);
  REP(i,n) cin>>a[i];

  if(n==1){
    cout<<1<<endl;
    return 0;
  }

  int c_max=0,c_min=0;
  REP(i,n){
    if(i==0){
      if(a[i]>a[i+1]) c_max++;
      if(a[i]<a[i+1]) c_min++;
      continue;
    }
    if(i==n-1){
      if(a[i-1]>a[i]) c_min++;
      if(a[i-1]<a[i]) c_max++;
      continue;
    }
    if(a[i-1]<a[i] && a[i]>a[i+1]) c_max++;
    if(a[i-1]>a[i] && a[i]<a[i+1]) c_min++;
  }
  cout<<min(c_max,c_min)+1<<endl;

  return 0;
}