#include<bits/stdc++.h>
using namespace std;
int n,i,an,t,a[111111],b[111111];
int main(){
	scanf("%d",&n);
	for(i=1;i<=n;i++)scanf("%d",&a[i]);
	for(i=1;i<=n;i++)if(a[i]!=a[i-1])b[++t]=a[i];
	for(i=3;i<=t;i++){
		if(b[i]>b[i-1]&&b[i-1]<b[i-2]||b[i]<b[i-1]&&b[i-1]>b[i-2])an++,i++;
	}
	printf("%d\n",an+1);
}
### Prompt

Please formulate 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<bits/stdc++.h>
using namespace std;
int n,i,an,t,a[111111],b[111111];
int main(){
	scanf("%d",&n);
	for(i=1;i<=n;i++)scanf("%d",&a[i]);
	for(i=1;i<=n;i++)if(a[i]!=a[i-1])b[++t]=a[i];
	for(i=3;i<=t;i++){
		if(b[i]>b[i-1]&&b[i-1]<b[i-2]||b[i]<b[i-1]&&b[i-1]>b[i-2])an++,i++;
	}
	printf("%d\n",an+1);
}
```