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.Text;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

class AtCoder
{
    const int MOD = 1000000007;
    
    public void Slove()
    {
        var n = int.Parse(Console.ReadLine());
        var array = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var ans = 
            Enumerable.Range(1, n - 2)            
            .Count(i => array[i - 1] < array[i] ^ array[i + 1] < array[i]);
        System.Console.WriteLine(ans);
    }
    static void Main()
    {
        var ac = new AtCoder();
        ac.Slove();
    }
}