#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main()
{
  int n;
  cin >> n;

  vector<int> a(n);
  for(int i = 0; i < n; i++){
    cin >> a[i];
  }

  a.erase(unique(a.begin(), a.end()), a.end());

  int ans = 1;
  for(int i = 2; i < a.size(); i++){
    if((a[i-2] < a[i-1] and a[i-1] > a[i]) or
      (a[i-2] > a[i-1] and a[i-1] < a[i])){
      ans++; i++;
    }
  }

  cout << ans << endl;

  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

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.

Examples

Input

6
1 2 3 2 2 1


Output

2


Input

9
1 2 1 2 1 2 1 2 1


Output

5


Input

7
1 2 3 2 1 999999999 1000000000


Output

3

### Response

```cpp
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main()
{
  int n;
  cin >> n;

  vector<int> a(n);
  for(int i = 0; i < n; i++){
    cin >> a[i];
  }

  a.erase(unique(a.begin(), a.end()), a.end());

  int ans = 1;
  for(int i = 2; i < a.size(); i++){
    if((a[i-2] < a[i-1] and a[i-1] > a[i]) or
      (a[i-2] > a[i-1] and a[i-1] < a[i])){
      ans++; i++;
    }
  }

  cout << ans << endl;

  return 0;
}

```