#include<iostream>
#include<algorithm>
#include<stack>
using namespace std;
const int M=100000+5;
int main()
{
	int n,a[M];
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	for(int i=1;i<n;i++){
		if(a[i]==a[i-1]){
			for(int j=i;j<n-1;j++)
				a[j]=a[j+1];
			n--;
		}	
	} 
	int t=1;
	for(int i=2;i<n;i++){
		if(a[i-1]<a[i-2] && a[i]>a[i-1]) {t++;i++;}
		else if(a[i-1]>a[i-2] && a[i]<a[i-1]) {t++;i++;}
	}
	cout<<t<<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<algorithm>
#include<stack>
using namespace std;
const int M=100000+5;
int main()
{
	int n,a[M];
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	for(int i=1;i<n;i++){
		if(a[i]==a[i-1]){
			for(int j=i;j<n-1;j++)
				a[j]=a[j+1];
			n--;
		}	
	} 
	int t=1;
	for(int i=2;i<n;i++){
		if(a[i-1]<a[i-2] && a[i]>a[i-1]) {t++;i++;}
		else if(a[i-1]>a[i-2] && a[i]<a[i-1]) {t++;i++;}
	}
	cout<<t<<endl;
	return 0; 
}
```