#include<bits/stdc++.h>
using namespace std;
int main(){
    int a,c=0;
    cin>>a;
    int b[a];
    for(int i=0;i<a;i++) cin>>b[i];
    for(int i=1;i<a-1;i++){
        if(b[i-1]<b[i]&&b[i]<b[i+1]) c++;
        if(b[i-1]>b[i]&&b[i]>b[i+1]) c++;
    }
    cout<<c;
}

### Prompt

Create a solution in Cpp for 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 main(){
    int a,c=0;
    cin>>a;
    int b[a];
    for(int i=0;i<a;i++) cin>>b[i];
    for(int i=1;i<a-1;i++){
        if(b[i-1]<b[i]&&b[i]<b[i+1]) c++;
        if(b[i-1]>b[i]&&b[i]>b[i+1]) c++;
    }
    cout<<c;
}

```