#include <bits/stdc++.h>
using namespace std;
int main()
  {int n, c{}; cin >> n;
  int P[n]; for (int &p : P) cin >> p;
  for (int i{1}; i < n - 1; ++i) c += P[i] == P[i - 1] + P[i] + P[i + 1] - min({P[i - 1], P[i], P[i + 1]}) - max({P[i - 1], P[i], P[i + 1]});
  cout << c;}
### 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, c{}; cin >> n;
  int P[n]; for (int &p : P) cin >> p;
  for (int i{1}; i < n - 1; ++i) c += P[i] == P[i - 1] + P[i] + P[i + 1] - min({P[i - 1], P[i], P[i + 1]}) - max({P[i - 1], P[i], P[i + 1]});
  cout << c;}
```