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>
#include <stdint.h>
#include <inttypes.h>
#include <string.h>
#include <math.h>

int main (void)
{
    intmax_t N, p[20];
    intmax_t ans = 0;

    scanf("%jd", &N);
    for (size_t i = 0; i < N; i++) {
        scanf("%jd", &p[i]);
    }

    for (size_t i = 1; i < (N - 1); i++) {
        if ((p[i - 1] > p[i]) && (p[i - 1] > p[i + 1]) && (p[i] >= p[i + 1])) {
            ans++;
        } else if ((p[i + 1] > p[i]) && (p[i + 1] > p[i - 1]) && (p[i] >= p[i - 1])) {
            ans++;
        }
    }

    printf("%jd\n", ans);

    return 0;
}