#include<iostream>
using namespace std;
int main(){
	int n,w=0;
	cin>>n;
	int a[n];
	for(int q=0;q<n;q++){
		cin>>a[q];
	}
	for(int q=1;q<n-1;q++){
		if((a[q]<=a[q-1]&&a[q]>a[q+1])||(a[q]<=a[q+1]&&a[q]>a[q-1]))w++;
	}
	cout<<w;
}
### Prompt

Create a solution in cpp for the following problem:

We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.

Print the number of elements p_i (1 < i < n) that satisfy the following condition:

* p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

Constraints

* All values in input are integers.
* 3 \leq n \leq 20
* p is a permutation of {1,\ 2,\ ...,\ n}.

Input

Input is given from Standard Input in the following format:


n
p_1 p_2 ... p_n


Output

Print the number of elements p_i (1 < i < n) that satisfy the condition.

Examples

Input

5
1 3 5 4 2


Output

2


Input

9
9 6 3 2 5 8 7 4 1


Output

5

### Response

```cpp
#include<iostream>
using namespace std;
int main(){
	int n,w=0;
	cin>>n;
	int a[n];
	for(int q=0;q<n;q++){
		cin>>a[q];
	}
	for(int q=1;q<n-1;q++){
		if((a[q]<=a[q-1]&&a[q]>a[q+1])||(a[q]<=a[q+1]&&a[q]>a[q-1]))w++;
	}
	cout<<w;
}
```