#include <bits/stdc++.h>
#define pi 3.14159
using namespace std;

int main()
 {
 	int n,i,j,d,c=0;
 	cin>>n;
 	int a[n];
 	for(i=0;i<n;i++)
 		cin>>a[i];
 		for(i=1;i<n-1;i++)
 		{
 			if((a[i]>a[i-1]&&a[i]<a[i+1])||(a[i]<a[i-1]&&a[i]>a[i+1]))
 				c++;
		 }
 	cout<<c<<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 <bits/stdc++.h>
#define pi 3.14159
using namespace std;

int main()
 {
 	int n,i,j,d,c=0;
 	cin>>n;
 	int a[n];
 	for(i=0;i<n;i++)
 		cin>>a[i];
 		for(i=1;i<n-1;i++)
 		{
 			if((a[i]>a[i-1]&&a[i]<a[i+1])||(a[i]<a[i-1]&&a[i]>a[i+1]))
 				c++;
		 }
 	cout<<c<<endl;	
 }
```