#include<bits/stdc++.h>
using namespace std;
int n,P[1000010],ans;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&P[i]);
	for(int i=2;i<=n-1;i++){
		int tmp=0;
		if(P[i]>P[i-1])tmp++;
		if(P[i]>P[i+1])tmp++;
		if(tmp==1)ans++;
	}
	cout<<ans;
	return 0;
}
### Prompt

Your task is to create 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;
int n,P[1000010],ans;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&P[i]);
	for(int i=2;i<=n-1;i++){
		int tmp=0;
		if(P[i]>P[i-1])tmp++;
		if(P[i]>P[i+1])tmp++;
		if(tmp==1)ans++;
	}
	cout<<ans;
	return 0;
}
```