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>
#define N_MAX 20

int main(void){
    // Your code here!
    int p[N_MAX];
    int n;
    
    scanf("%d", &n);
    for(int i = 0; i < n; i ++){
        scanf("%d", p+i);
    }
    
    int num = 0;
    for(int i = 1; i < n-1; i ++){
        int p1 = p[i-1];
        int p2 = p[i];
        int p3 = p[i+1];
        num += (p1 < p2 && p2 < p3) || (p3 < p2 && p2 < p1);
    }
    printf("%d", num);
}