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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

var count = 0;
var pass = 0;

function Main(input) {

	input = input.split("\n");
	
    var n = parseInt(input[0]);
    var p = input[1].split(" ");
    
    for(var i = 0;i < n-2;i++){
        if(p[i]<p[i+1]&&p[i+1]<p[i+2]){
            if(p[i]===p[i+1]||p[i+1]===p[i+2]||p[i+1]===p[i+2]){
                pass++;
            }else{
                count++;
            }
        }else if(p[i]>p[i+1]&&p[i+1]>p[i+2]){
            if(p[i]===p[i+1]||p[i+1]===p[i+2]||p[i+1]===p[i+2]){
                pass++;
            }else{
                count++;
            }
        }
    }
    
    
    console.log(count);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));