#include <bits/stdc++.h>
using namespace std;

int main(){

 int n,p[30],ans=0;
  
  cin>>n;
  
  for(int i=0;i<n;i++){
  cin>>p[i];
  }
  
  for(int j=1;j<n-1;j++){
   if(p[j]>p[j-1]&&p[j+1]>p[j]||
     		p[j]<p[j-1]&&p[j+1]<p[j]){
   ans++;
   }
  }
  cout<<ans;
}
### Prompt

Please formulate 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>
using namespace std;

int main(){

 int n,p[30],ans=0;
  
  cin>>n;
  
  for(int i=0;i<n;i++){
  cin>>p[i];
  }
  
  for(int j=1;j<n-1;j++){
   if(p[j]>p[j-1]&&p[j+1]>p[j]||
     		p[j]<p[j-1]&&p[j+1]<p[j]){
   ans++;
   }
  }
  cout<<ans;
}
```