#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n,p[20]; cin>>n;
	rep(i,n) cin>>p[i];

	int ans=0;
	rep(i,n-2) if((p[i]<p[i+1] && p[i+1]<p[i+2]) || (p[i]>p[i+1] && p[i+1]>p[i+2])) ans++;
	cout<<ans<<endl;

	return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n,p[20]; cin>>n;
	rep(i,n) cin>>p[i];

	int ans=0;
	rep(i,n-2) if((p[i]<p[i+1] && p[i+1]<p[i+2]) || (p[i]>p[i+1] && p[i+1]>p[i+2])) ans++;
	cout<<ans<<endl;

	return 0;
}

```