#include<stdio.h>
int main()
{
	int n,i,cnt=0;
	int a[100]={};
	while(~scanf("%d",&n)){
		for(i=0;i<n;i++){
			scanf("%d",&a[i]);
		}for(i=0;i<n-2;i++){
			if(a[i+1]>a[i]&&a[i+1]<a[i+2]||a[i+1]<a[i]&&a[i+1]>a[i+2]){
				cnt++;
			}
		}printf("%d\n",cnt);
		cnt=0;
	}
} 
### Prompt

Construct a cpp code solution to the problem outlined:

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 main()
{
	int n,i,cnt=0;
	int a[100]={};
	while(~scanf("%d",&n)){
		for(i=0;i<n;i++){
			scanf("%d",&a[i]);
		}for(i=0;i<n-2;i++){
			if(a[i+1]>a[i]&&a[i+1]<a[i+2]||a[i+1]<a[i]&&a[i+1]>a[i+2]){
				cnt++;
			}
		}printf("%d\n",cnt);
		cnt=0;
	}
} 
```