#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int main(){
	int n, ans = 1;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	a.erase(unique(begin(a), end(a)), end(a));
	for(int i = 2; i < a.size(); i++){
		int b, c;
		b = a[i - 2] - a[i - 1];
		c = a[i - 1] - a[i];
		if((b > 0 && c < 0) || (b < 0 && c > 0)){
			ans++;
			i++;
		}
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Your challenge is to write 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, ans = 1;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	a.erase(unique(begin(a), end(a)), end(a));
	for(int i = 2; i < a.size(); i++){
		int b, c;
		b = a[i - 2] - a[i - 1];
		c = a[i - 1] - a[i];
		if((b > 0 && c < 0) || (b < 0 && c > 0)){
			ans++;
			i++;
		}
	}
	cout << ans << endl;
	return 0;
}
```