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

int main() {
  int n,ans=0;
  cin>>n;
  vector<int> p(n);
  for(int i=0; i<n; i++) cin>>p[i];
  for(int i=1; i<n-1; i++) {
    if(p[i-1]<p[i]) {
      if(p[i]<p[i+1]) ans++;
    }
    else if(p[i]>p[i+1]) ans++;
  }
  cout<<ans;
}
### Prompt

Your task is to create 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,ans=0;
  cin>>n;
  vector<int> p(n);
  for(int i=0; i<n; i++) cin>>p[i];
  for(int i=1; i<n-1; i++) {
    if(p[i-1]<p[i]) {
      if(p[i]<p[i+1]) ans++;
    }
    else if(p[i]>p[i+1]) ans++;
  }
  cout<<ans;
}
```