#include <iostream>

using namespace std;

int main()
{ int n,c=0;
  cin>>n;
  int arr[n];
   for(int i=0 ;i<n ;i++) cin>>arr[i];
    for(int i=1;i<n-1;i++) if(((arr[i]>arr[i-1])&&(arr[i]<arr[i+1]))||((arr[i]<arr[i-1])&&(arr[i]>arr[i+1]))) c++;
    cout<<c;
    return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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,c=0;
  cin>>n;
  int arr[n];
   for(int i=0 ;i<n ;i++) cin>>arr[i];
    for(int i=1;i<n-1;i++) if(((arr[i]>arr[i-1])&&(arr[i]<arr[i+1]))||((arr[i]<arr[i-1])&&(arr[i]>arr[i+1]))) c++;
    cout<<c;
    return 0;
}

```