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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>

int getAns(int, int a[]);

int main() {
    int n;
    int p[20] = {0};
    
    scanf("%d", &n);
    for (int i = 0; i < n - 1; i++) {
        scanf("%d ", p + i);
    }
    scanf("%d", p + n - 1);

    printf("%d", getAns(n, p));

    return 0;
}

int getAns(int n, int p[]) {
    int count = 0;

    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            for (int k = k + 1; k < n; k++) {
                if (p[i] < p[j] && p[j] < p[k]) {
                    count++;
                } else if (p[i] > p[j] && p[j] > p[k]) {
                    count++;
                }
            }
        }
    }

    return count;
}