#include <iostream>
using namespace std;

int main() {
	int n;
	cin >> n;
	int p1, p2, p3;
	cin >> p1 >> p2;
	int ans = 0;
	for (int i = 2; i < n; i++) {
		cin >> p3;
		if ((p1 < p2 && p2 < p3) || (p3 < p2 && p2 < p1)) ans++;
		p1 = p2;
		p2 = p3;
	}
	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 <iostream>
using namespace std;

int main() {
	int n;
	cin >> n;
	int p1, p2, p3;
	cin >> p1 >> p2;
	int ans = 0;
	for (int i = 2; i < n; i++) {
		cin >> p3;
		if ((p1 < p2 && p2 < p3) || (p3 < p2 && p2 < p1)) ans++;
		p1 = p2;
		p2 = p3;
	}
	cout << ans << endl;
}

```