#include<iostream>
using namespace std;

int main(){
  int n,i,c=0; cin>>n;
  int s[n];
  for(i=0;i<n;i++) cin>>s[i];
  
  for(i=0;i<n-2;i++){
    if(s[i]<s[i+1] && s[i+1]<s[i+2])c += 1;
    if(s[i]>s[i+1] && s[i+1]>s[i+2])c += 1;
  }
  
  cout<<c<<endl;
  return 0;
}

### 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<iostream>
using namespace std;

int main(){
  int n,i,c=0; cin>>n;
  int s[n];
  for(i=0;i<n;i++) cin>>s[i];
  
  for(i=0;i<n-2;i++){
    if(s[i]<s[i+1] && s[i+1]<s[i+2])c += 1;
    if(s[i]>s[i+1] && s[i+1]>s[i+2])c += 1;
  }
  
  cout<<c<<endl;
  return 0;
}

```