Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

2

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<utility>
#include<algorithm> // sort
#include<map> // pair
#include<cmath>
using namespace std;
using ll = long long;
const ll mod = 1e9+7;

int main(){
  int n;
  cin >> n;
  int a[n];
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  int count=0;
  for(int i=0;i<n-2;i++){
    if(a[i] < a[i+1] && a[i+1] < a[i+2]){
      count++;
    }else if(a[i] > a[i+1] && a[i+1] > a[i+2]){
      count++;
    }
  }
  cout << count;
}