#include<iostream>
using namespace std;
int main(){
  int N;
  cin >> N;
  int p[N], temp[3];
  int counter = 0;
  for(int i=0; i<N; ++i){
    cin >> p[i];
  }
  for(int i=1; i<N-1; ++i){
  	if((p[i-1]-p[i])*(p[i]-p[i+1]) >0) counter++;
  }
  cout << counter << 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;
  cin >> N;
  int p[N], temp[3];
  int counter = 0;
  for(int i=0; i<N; ++i){
    cin >> p[i];
  }
  for(int i=1; i<N-1; ++i){
  	if((p[i-1]-p[i])*(p[i]-p[i+1]) >0) counter++;
  }
  cout << counter << endl;
  return 0;
}
```