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 <algorithm>
using namespace std;

int main(void) {
  int n;
  cin >> n;
  
  int p[n];
  for(int i = 0; i < n; i++) {
  	cin >> p[i];
  }
  
  int count = 0;
  int array[3];
  for(int i = 1; i < n - 1; i++) {
  	int p1 = p[i-1];
    int p2 = p[i];
    int p3 = p[i+1];
    array[0] = p1;
    array[1] = p2;
    array[2] = p3;
    
    sort(array, array + 3);
    
    if(array[1] == p2 && (array[1] != array[0] && array[1] != array[2])) {
      count++;
    }
  }
  
  cout << count << endl;
  return 0;
}