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


int main() {
	int N;
	cin >> N;
	int ans = 1;
	vector<int> A(1,0);
	cin >> A[0];
	for (int i = 1; i < N; i++) {
		int buf;
		cin >> buf;
		if (A.back() != buf) A.push_back(buf);
	}
	N = A.size();
	int i = 0;
	while (i < N - 2) {
		if (((A[i + 2] < A[i + 1]) && (A[i + 1] > A[i])) || ((A[i + 2] > A[i + 1]) && (A[i + 1] < A[i]))) {
			ans++;
			i++;
		}
		i++;
	}
	cout << ans;
}
### 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>
using namespace std;


int main() {
	int N;
	cin >> N;
	int ans = 1;
	vector<int> A(1,0);
	cin >> A[0];
	for (int i = 1; i < N; i++) {
		int buf;
		cin >> buf;
		if (A.back() != buf) A.push_back(buf);
	}
	N = A.size();
	int i = 0;
	while (i < N - 2) {
		if (((A[i + 2] < A[i + 1]) && (A[i + 1] > A[i])) || ((A[i + 2] > A[i + 1]) && (A[i + 1] < A[i]))) {
			ans++;
			i++;
		}
		i++;
	}
	cout << ans;
}
```