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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

int main()
{
	int n, k, l, c;
	int P[20];
	c = 0;
	scanf("%d", &n);
	for (k = 1; k < n + 1; k++)
	{
		scanf("%d", &P[k]);
	}
	P[0] = 0;
	for (l = 1; l < n - 1; l++)
	{
		if (P[l] < P[l + 1])
		{
			if (P[l + 1] <= P[l + 2])
			{
				c++;
			}
		}
		else if (P[l + 1] >= P[l + 2] && P[l] != P[l + 2]) 
		{
			c++;
		}
	}
	printf("%d", c);
	return 0;
}