#include<iostream>
#include<vector>
using namespace std;
#define pb push_back
int main(){
	int n,ans=1;
	vector<int> a;
	cin>>n;
	for(int i=0;i<n;++i){
		int v;
		cin>>v;
		if(a.empty()||a[a.size()-1]!=v){
			a.pb(v);
		}
	}
	if(a.size()==1){
		cout<<1<<endl;
		return 0;
	}
	for(int i=0;i<a.size()-2;++i){
		if((a[i]<a[i+1]&&a[i+1]>a[i+2])||(a[i]>a[i+1]&&a[i+1]<a[i+2])){
			++ans;
			++i;
		}
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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;
#define pb push_back
int main(){
	int n,ans=1;
	vector<int> a;
	cin>>n;
	for(int i=0;i<n;++i){
		int v;
		cin>>v;
		if(a.empty()||a[a.size()-1]!=v){
			a.pb(v);
		}
	}
	if(a.size()==1){
		cout<<1<<endl;
		return 0;
	}
	for(int i=0;i<a.size()-2;++i){
		if((a[i]<a[i+1]&&a[i+1]>a[i+2])||(a[i]>a[i+1]&&a[i+1]<a[i+2])){
			++ans;
			++i;
		}
	}
	cout<<ans<<endl;
	return 0;
}
```