#include<bits/stdc++.h>
using namespace std;
int main(){
  int N;
  cin>>N;
  int A,B,C;
  cin>>A>>B;
  int count=0;
  for(int i=2;i<N;i++){
    cin>>C;
    if(A<B&&B<C) count++;
    else if(C<B&&B<A) count++;
    A=B;
    B=C;
    }
  cout<<count<<endl;
  }
### Prompt

Please create a solution in cpp 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;
  cin>>N;
  int A,B,C;
  cin>>A>>B;
  int count=0;
  for(int i=2;i<N;i++){
    cin>>C;
    if(A<B&&B<C) count++;
    else if(C<B&&B<A) count++;
    A=B;
    B=C;
    }
  cout<<count<<endl;
  }
```