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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int maxcal (int max,int i){
  if(max < i){
    max = i;
  }
  return max;
}

int  mincal (int min,int i){
  if(min > i){
    min = i;
  }
  return min;
}

int main(){
  int n = 0;
  int max = 0;
  int min = 21;
  int count = 0;
  char *end1, *end2;
  scanf("%d",&n);
  int a[n+1];
  char b[3*n + 1];
  scanf("%*c%[^\n]%*c", b);
  //printf("%c\n", b[0]);
  //printf("%c\n", b[1]);
  //printf("%c\n", b[2]);
  // for(int i = 0; i < n; i++){
  a[0] = strtol(b, &end1, 10);
  for(int i = 1; i < n; i++){
    a[i] = strtol(end1, &end2, 10);
    end1 = end2;
  }
  for(int j = 0; j < n - 2; j++){
    //printf("%d\n",a[j]);
    max = a[j];
    min = a[j];
    max = maxcal(max, a[j + 1]);
    min = mincal(min, a[j + 1]);
    max = maxcal(max, a[j + 2]);
    min = mincal(min, a[j + 2]);
    //printf("%d %d\n", max, min);
    if(a[j + 1] != max && a[j + 1] != min){
      count++;
    }
}
printf("%d\n", count);
    return 0;
}