#include <bits/stdc++.h>
using namespace std;

const int N = 100010;
int a[N],f[N][2],n;
int main(){
	scanf("%d",&n);
	for(int i =1;i<=n;i++)scanf("%d",a+i); 
	f[1][0]=f[1][1]=1;
	for(int i =2;i<=n;i++){
		if(a[i]>a[i-1]) f[i][0]=min(f[i-1][0],f[i-1][1])+1; else f[i][0]=min(f[i-1][0],f[i-1][1]+1);
		
		if(a[i]<a[i-1]) f[i][1]=min(f[i-1][0],f[i-1][1])+1; else f[i][1]=min(f[i-1][1],f[i-1][0]+1);
		
	}
	cout<<min(f[n][0],f[n][1])<<endl;
	return 0;
}
### Prompt

In CPP, your task is to solve 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 <bits/stdc++.h>
using namespace std;

const int N = 100010;
int a[N],f[N][2],n;
int main(){
	scanf("%d",&n);
	for(int i =1;i<=n;i++)scanf("%d",a+i); 
	f[1][0]=f[1][1]=1;
	for(int i =2;i<=n;i++){
		if(a[i]>a[i-1]) f[i][0]=min(f[i-1][0],f[i-1][1])+1; else f[i][0]=min(f[i-1][0],f[i-1][1]+1);
		
		if(a[i]<a[i-1]) f[i][1]=min(f[i-1][0],f[i-1][1])+1; else f[i][1]=min(f[i-1][1],f[i-1][0]+1);
		
	}
	cout<<min(f[n][0],f[n][1])<<endl;
	return 0;
}
```