#include<iostream>
using namespace std;

int main(){
  int i,n,count=0;
  cin >> n;
  int p[20];
  for(i=0;i<n;i++) cin >> p[i];
  for(i=1;i<n-1;i++){
    if((p[i-1]<p[i] && p[i]<p[i+1]) || (p[i-1]>p[i] && p[i]>p[i+1])) count++;
  }
  
  cout << count << endl;
}
    
### Prompt

In Cpp, your task is to solve 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 i,n,count=0;
  cin >> n;
  int p[20];
  for(i=0;i<n;i++) cin >> p[i];
  for(i=1;i<n-1;i++){
    if((p[i-1]<p[i] && p[i]<p[i+1]) || (p[i-1]>p[i] && p[i]>p[i+1])) count++;
  }
  
  cout << count << endl;
}
    
```