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.Text;

namespace AtCoder
{
	public class Program
	{
		// ABC132-A ok
		static void Main(string[] args)
		{
			string n = Console.ReadLine();
			string str = Console.ReadLine();

			int[] vs = str.Split().Select(p => int.Parse(p)).ToArray();
			int count = 0;
			for (int i = 0; i < vs.Length - 2; i++) {
				int p1 = vs[i], p2 = vs[i + 1], p3 = vs[i + 2];
				if ((p1 < p2 && p2 < p3) || (p3 < p2 && p2 < p1)) {
					count++;
				}
			}
			Console.WriteLine(count);
		}
	}
}