#include<bits/stdc++.h>
using namespace std;
int main()
{
 int n;
 cin >> n;
 int a[n],i;
 for(i=0;i<n;i++)
 cin >> a[i];
 int c=0;
  for(i=1;i<n-1;i++)
  {
      if((a[i]>a[i-1] && a[i]<a[i+1]) || (a[i]<a[i-1] && a[i]>a[i+1]))
      c++;
  }
  cout << c;
  return 0;   
}
### 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;
 cin >> n;
 int a[n],i;
 for(i=0;i<n;i++)
 cin >> a[i];
 int c=0;
  for(i=1;i<n-1;i++)
  {
      if((a[i]>a[i-1] && a[i]<a[i+1]) || (a[i]<a[i-1] && a[i]>a[i+1]))
      c++;
  }
  cout << c;
  return 0;   
}
```