#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int N=100010;
int n,ans=1,cnt=0;
int a[N];
int main()
{
	scanf("%d",&n);
	for(int k=1;k<=n;k++)
	{
		int x;
		scanf("%d",&x);
		if(x!=a[cnt]) a[++cnt]=x;
	}
	for(int k=2;k<cnt;k++)
	{
		if(a[k]>a[k-1]&&a[k]>a[k+1]) k++,ans++;
		else if(a[k]<a[k-1]&&a[k]<a[k+1]) k++,ans++;
	}
	printf("%d",ans);
	return 0;
}
### 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<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
const int N=100010;
int n,ans=1,cnt=0;
int a[N];
int main()
{
	scanf("%d",&n);
	for(int k=1;k<=n;k++)
	{
		int x;
		scanf("%d",&x);
		if(x!=a[cnt]) a[++cnt]=x;
	}
	for(int k=2;k<cnt;k++)
	{
		if(a[k]>a[k-1]&&a[k]>a[k+1]) k++,ans++;
		else if(a[k]<a[k-1]&&a[k]<a[k+1]) k++,ans++;
	}
	printf("%d",ans);
	return 0;
}
```