#include <bits/stdc++.h>
using namespace std;
 
int main() {
  int n, ans = 0;
  cin >> n;
  int a, b, c;
  cin >> a >> b;
  for (int i = 1; i < n - 1; i++) {
    cin >> c;
    if (a < b && b < c || c < b && b < a) {
      ans++;
    }
    a = b, b = c;
  }
  cout << ans << endl;
}
### Prompt

In cpp, your task is to solve 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, ans = 0;
  cin >> n;
  int a, b, c;
  cin >> a >> b;
  for (int i = 1; i < n - 1; i++) {
    cin >> c;
    if (a < b && b < c || c < b && b < a) {
      ans++;
    }
    a = b, b = c;
  }
  cout << ans << endl;
}
```