#include <iostream>
using namespace std;
int a[25];
int main()
{
	int n,m=0;
	cin>>n;
	for (int i = 0;i < n;i++)
	{
		cin >> a[i];
	}
	for (int i = 0;i < n-2;i++)
	{
		if ((a[i] < a[i + 1] && a[i + 1] < a[i + 2])||(a[i]>a[i+1]&&a[i+1]>a[i+2])) m++;
	}
	cout << m << '\n';
}
### 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 a[25];
int main()
{
	int n,m=0;
	cin>>n;
	for (int i = 0;i < n;i++)
	{
		cin >> a[i];
	}
	for (int i = 0;i < n-2;i++)
	{
		if ((a[i] < a[i + 1] && a[i + 1] < a[i + 2])||(a[i]>a[i+1]&&a[i+1]>a[i+2])) m++;
	}
	cout << m << '\n';
}
```