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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class Main {
    static final int MAX = 100100;
    InputStream in = System.in;
    PrintStream out = System.out;
    // static int dp[][] = new int[MAX][MAX];
    static int p[] = new int[20];

    public void _main(String[] args) {
        Scanner sc = new Scanner(in);
        int n = sc.nextInt();
        int cnt=0;
        for (int i=0;i<n;i++) {
            p[i] = sc.nextInt();
        }
        for (int i=1;i<n-1;i++) {
            if (p[i-1] < p[i] && p[i] < p[i+1]) cnt++;
            else if (p[i+1]<p[i]&&p[i]<p[i-1]) cnt++;
        }
        out.println(cnt);
    }

    public static void main(String[] args) {
        new Main()._main(args);
    }
}