#include<bits/stdc++.h>
int main()
{
	int n;
	std::cin>>n;
	int arr[n];
	for(int i=0;i<n;i++)
	std::cin>>arr[i];
	int j=0;
	for(int i=1;i<n-1;i++)
	{
		if(arr[i]<arr[i-1] and arr[i]>arr[i+1])
		j++;
		else if(arr[i]>arr[i-1] and arr[i]<arr[i+1])
		j++;
	}
	std::cout<<j<<"\n";
}
### Prompt

Your challenge is to write a Cpp solution to 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<bits/stdc++.h>
int main()
{
	int n;
	std::cin>>n;
	int arr[n];
	for(int i=0;i<n;i++)
	std::cin>>arr[i];
	int j=0;
	for(int i=1;i<n-1;i++)
	{
		if(arr[i]<arr[i-1] and arr[i]>arr[i+1])
		j++;
		else if(arr[i]>arr[i-1] and arr[i]<arr[i+1])
		j++;
	}
	std::cout<<j<<"\n";
}
```