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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading.Tasks;

class Program {
    static void Main (string[] args) {
          

        int n = int.Parse(Console.ReadLine ());
        string[] p = Console.ReadLine ().Split(' ');

        int ans = 0;
        for(int i=1;i<n -1 ;i++){
            int bef = int.Parse(p[i-1]);
            int cur = int.Parse(p[i]);
            int aft = int.Parse(p[i+1]);
            if(bef < cur && cur < aft || aft < cur && cur < bef) ans++;
        }
        Console.WriteLine(ans);
    }
}