#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long;
int main() {
  int N, ans = 1;
  cin >> N;
  vector<int> A;
  for (int i = 0, t; i < N; i++) {
    cin >> t;
    if (A.empty() || t != A.back()) A.push_back(t);
  }
  for (int i = 1; i < A.size() - 1; i++) {
    if (A[i] > max(A[i - 1], A[i + 1]) || A[i] < min(A[i - 1], A[i + 1])) {
      ans++;
      i++;
    }
  }
  cout << ans << endl;
}

### Prompt

Create a solution in CPP for 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;
using ll = long long;
int main() {
  int N, ans = 1;
  cin >> N;
  vector<int> A;
  for (int i = 0, t; i < N; i++) {
    cin >> t;
    if (A.empty() || t != A.back()) A.push_back(t);
  }
  for (int i = 1; i < A.size() - 1; i++) {
    if (A[i] > max(A[i - 1], A[i + 1]) || A[i] < min(A[i - 1], A[i + 1])) {
      ans++;
      i++;
    }
  }
  cout << ans << endl;
}

```