#include <stdio.h>
int a[50];
int main()
{
	int n,m,i,j,k,s,t;
	while(~scanf("%d",&n))
	{
		for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
		m=0;
		for(i=2;i<=n-1;i++)
		{
			if(((a[i-1]-a[i])*(a[i+1]-a[i]))<=0)
			m++;
		}
		printf("%d\n",m);
	}
	return 0;
} 
### 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 <stdio.h>
int a[50];
int main()
{
	int n,m,i,j,k,s,t;
	while(~scanf("%d",&n))
	{
		for(i=1;i<=n;i++)
		scanf("%d",&a[i]);
		m=0;
		for(i=2;i<=n-1;i++)
		{
			if(((a[i-1]-a[i])*(a[i+1]-a[i]))<=0)
			m++;
		}
		printf("%d\n",m);
	}
	return 0;
} 
```