#include<bits/stdc++.h>
using namespace std;;
int main(){
  int N,jug=0;
  cin >> N;
  vector<int> su(N);
  for(int i=0;i<N;i++)cin >> su[i];
  for(int i=1;i<N-1;i++){
    if(su[i]>su[i-1]&&su[i+1]>su[i]||su[i]>su[i+1]&&su[i-1]>su[i])jug++;
  }
  cout << jug << endl;
}
 
### Prompt

Create a solution in CPP for 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,jug=0;
  cin >> N;
  vector<int> su(N);
  for(int i=0;i<N;i++)cin >> su[i];
  for(int i=1;i<N-1;i++){
    if(su[i]>su[i-1]&&su[i+1]>su[i]||su[i]>su[i+1]&&su[i-1]>su[i])jug++;
  }
  cout << jug << endl;
}
 
```