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.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

    private static PrintWriter out;

    private static <T> void mprintln(T ... ar){
        for(T i: ar) out.print(i + " ");
        out.println();
    }

    public static void main(String[] args) throws FileNotFoundException{

        // Input from file
        // File inputFile = new File("JavaFile.txt");
        // File outputFile = new File("JavaOutputFile.txt");
        // FileReader fileReader = new FileReader(inputFile);
        // Here it ends

        MyScanner sc = new MyScanner();
        // MyScanner sc = new MyScanner(fileReader);

        out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
        // out = new PrintWriter(new PrintStream(outputFile)); // Output to file

        getAns(sc);

        out.close();
    }

    /*
     *Don't use builtin function (Math.ceil)
     */

    static final long MOD = (long) (1e9 + 7);

    private static void getAns(MyScanner sc){
        int n = sc.ni();
        int[] ar = sc.niArr0(n);
        int ans = 0;

        for(int i = 1; i < n - 1; i++){
            if((ar[i] < ar[i - 1] && ar[i] > ar[i + 1]) || (ar[i] > ar[i - 1] && ar[i] < ar[i + 1])) ++ans;
        }

        out.println(ans);
    }

    static class MyScanner{
        BufferedReader br;
        StringTokenizer st;

        MyScanner(FileReader fileReader){
            br = new BufferedReader(fileReader);
        }

        MyScanner(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nn(){
            while(st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine(){
            String ans = "";
            try {
                ans = br.readLine();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return ans;
        }

        char nc(){
            return nn().charAt(0);
        }

        int ni(){
            return Integer.parseInt(nn());
        }

        long nl(){
            return Long.parseLong(nn());
        }

        double nd(){
            return Double.parseDouble(nn());
        }

        int[] niArr0(int n){
            int[] ar = new int[n];
            for(int i = 0; i < n; i++) ar[i] = ni();
            return ar;
        }

        int[] niArr1(int n){
            int[] ar = new int[n + 1];
            for(int i = 1; i <= n; i++) ar[i] = ni();
            return ar;
        }

        long[] nlArr0(int n){
            long[] ar = new long[n];
            for(int i = 0; i < n; i++) ar[i] = nl();
            return ar;
        }

        long[] nlArr1(int n){
            long[] ar = new long[n + 1];
            for(int i = 1; i <= n; i++) ar[i] = nl();
            return ar;
        }
    }
}