#include <bits/stdc++.h>
using namespace std;
bool bemid(int a,int b,int c){
	return b<a&&a<c || b>a&&a>c;
}
int main(){
	int n;cin>>n;
	int p[29];
	for(int i=1;i<=n;++i)cin>>p[i];
	int c=0;
	for(int i=2;i<n;++i){
		if(bemid(p[i],p[i-1],p[i+1]))c++;
	}
	cout<<c;
    return 0;
}
### Prompt

Your challenge is to write 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 <bits/stdc++.h>
using namespace std;
bool bemid(int a,int b,int c){
	return b<a&&a<c || b>a&&a>c;
}
int main(){
	int n;cin>>n;
	int p[29];
	for(int i=1;i<=n;++i)cin>>p[i];
	int c=0;
	for(int i=2;i<n;++i){
		if(bemid(p[i],p[i-1],p[i+1]))c++;
	}
	cout<<c;
    return 0;
}
```