#include "bits/stdc++.h"
using ll = long long;
using namespace std;
int main(){
ll n;
cin>>n;
ll ans=0;
vector<ll> p(n);

ll tmp;
for(int i=0;i<n;i++){
cin>>p[i];
}

for(int i=1;i<n-1;i++){
if(p[i-1]<p[i]&&p[i]<p[i+1]||p[i+1]<p[i]&&p[i]<p[i-1])
ans++;
}
cout<<ans<<endl;
}

### Prompt

Please create a solution in Cpp to 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 ll = long long;
using namespace std;
int main(){
ll n;
cin>>n;
ll ans=0;
vector<ll> p(n);

ll tmp;
for(int i=0;i<n;i++){
cin>>p[i];
}

for(int i=1;i<n-1;i++){
if(p[i-1]<p[i]&&p[i]<p[i+1]||p[i+1]<p[i]&&p[i]<p[i-1])
ans++;
}
cout<<ans<<endl;
}

```