#include <cstdio>
#define N 100010
int n,a[N],f[N];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%d",&a[i]);
	int op=-1;
	for(int i=1;i<=n;++i){
		if(op==0 && a[i]==a[i-1]) f[i]=f[i-1],op=0;
		else if((op==0 || op==1) && a[i]>=a[i-1]) f[i]=f[i-1],op=1;
		else if((op==0 || op==2) && a[i]<=a[i-1]) f[i]=f[i-1],op=2;
		else{
			f[i]=f[i-1]+1;
			op=0;
		}
	}
	printf("%d\n",f[n]);
	return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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 <cstdio>
#define N 100010
int n,a[N],f[N];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%d",&a[i]);
	int op=-1;
	for(int i=1;i<=n;++i){
		if(op==0 && a[i]==a[i-1]) f[i]=f[i-1],op=0;
		else if((op==0 || op==1) && a[i]>=a[i-1]) f[i]=f[i-1],op=1;
		else if((op==0 || op==2) && a[i]<=a[i-1]) f[i]=f[i-1],op=2;
		else{
			f[i]=f[i-1]+1;
			op=0;
		}
	}
	printf("%d\n",f[n]);
	return 0;
}
```