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

int main(){
  int n,cnt=0;
  cin >> n;
  int a[n];
  for(int i=0;i<n;i++)
    cin >> a[i];
  for(int i=0;i<n-2;i++){
    if((a[i]<a[i+1]&&a[i+1]<a[i+2])||(a[i]>a[i+1]&&a[i+1]>a[i+2]))
      cnt++;
  }
  cout << cnt << endl;
}

### Prompt

Please formulate 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,cnt=0;
  cin >> n;
  int a[n];
  for(int i=0;i<n;i++)
    cin >> a[i];
  for(int i=0;i<n-2;i++){
    if((a[i]<a[i+1]&&a[i+1]<a[i+2])||(a[i]>a[i+1]&&a[i+1]>a[i+2]))
      cnt++;
  }
  cout << cnt << endl;
}

```