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

int main() {
  int n;
  cin>>n;
  vector<int> p(n);
  for (int i=0; i<n; i++)
    cin>>p.at(i);
  
  int z=0;
  for (int i=1; i<n-1; i++) {
    if ( (p.at(i-1)-p.at(i)) * (p.at(i+1)-p.at(i)) < 0 )
      z++;
  }
  cout<< z <<endl;
}

### 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;
  vector<int> p(n);
  for (int i=0; i<n; i++)
    cin>>p.at(i);
  
  int z=0;
  for (int i=1; i<n-1; i++) {
    if ( (p.at(i-1)-p.at(i)) * (p.at(i+1)-p.at(i)) < 0 )
      z++;
  }
  cout<< z <<endl;
}

```