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

int main() {
	int N, P[20], ANS = 0;
	cin >> N;
	for (int i = 0; i < N; i++) cin >> P[i];
	for (int i = 0; i < N - 2; i++) {
		if ((P[i + 1] - P[i]) * (P[i + 2] - P[i + 1]) > 0) ANS++;
	}
	cout << ANS;
}
### 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, P[20], ANS = 0;
	cin >> N;
	for (int i = 0; i < N; i++) cin >> P[i];
	for (int i = 0; i < N - 2; i++) {
		if ((P[i + 1] - P[i]) * (P[i + 2] - P[i + 1]) > 0) ANS++;
	}
	cout << ANS;
}
```