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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {

	static Scanner scanner;

	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    int N=gi();
	    int[] P=new int[N];

        for(int i=0; i<N; i++) {
        	P[i]=gi();
        }

        int c=0;   
        for (int i=1; i<N-1; i++) {
        	if((P[i]>P[i-1] && P[i]<P[i+1]) || (P[i]<P[i-1] && P[i]>P[i+1])) {
        		c++;
        	}
        }
        

        System.out.print(c);

//        if (b>=1 && b<=12) {
//        	if(a>=1 && a<=12) {
//        	    System.out.println("AMBIGUOUS");
//        	} else {
//        		System.out.println("MMYY");
//        	}
//        }else {
//        	if(a>=1 && a<=12) {
//        	    System.out.println("YYMM");
//        	} else {
//        		System.out.println("NA");
//        	}
//        }
	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}
}