#include <iostream> 
#include <vector>
using namespace std;

int main() {
	int n;
	vector<int> p;
	cin >> n;

	for(int i = 0;i<n;i++){
		int a;
		cin >> a;
		p.push_back(a);
	}
	int ans=0;
	for(int i = 2;i<n;i++){
		if((p[i-2]-p[i-1])*(p[i-1]-p[i])>0)ans++;
	}
	cout << ans;
}

### 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 <iostream> 
#include <vector>
using namespace std;

int main() {
	int n;
	vector<int> p;
	cin >> n;

	for(int i = 0;i<n;i++){
		int a;
		cin >> a;
		p.push_back(a);
	}
	int ans=0;
	for(int i = 2;i<n;i++){
		if((p[i-2]-p[i-1])*(p[i-1]-p[i])>0)ans++;
	}
	cout << ans;
}

```