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 main() {
    int n;
    scanf("%d", &n);
    int *p = malloc((n + 1) * sizeof(int));
    for (int i = 1; i <= n; i++) {
        scanf("%d", &p[i]);
    }
    int ans = 0;
    for (int i = 2; i <= n - 1; i++) {
        int dif_1 = p[i] - p[i-1];
        int dif_2 = p[i] - p[i+1];
        if ((dif_1 < 0 && dif_2 > 0) || (dif_1 > 0 && dif_2 < 0))
            ans++;
    }
    printf("%d\n", ans);
    return 0;
}