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: Wrong Answer)

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

int main(void){
	
	char n_str[5];
	int n;
	char p_str[60];
	char *p_tmp;
	int p[20];
	int c;
	
	int ans;
	
	fgets(n_str,sizeof(n_str),stdin);	
	fgets(p_str,sizeof(p_str), stdin);

	printf("n_str = %s\n", n_str);
	printf("p_str = %s\n", p_str);
	
	n = strtol(n_str,NULL,10);

	printf("n = %d\n", n);
	
	for(c=0;c<n;c++)
	{
		if(c==0)
			p_tmp = strtok(p_str," ");
		else
			p_tmp = strtok(NULL," ");
		p[c] = strtol(p_tmp,NULL,10);
	}
	
	for(c=0;c<n;c++)
	{
		printf("p[%d] = %d\n",c,p[c]);
	}
	
	ans = 0;
	
	for(c=0;c<(n-2);c++)
	{
		if(p[c]<p[c+1] && p[c+1] < p[c+2])
			ans++;
		
		if(p[c+2]<p[c+1] && p[c+1] < p[c])
			ans++;
	}
	
	printf("%d",ans);

	return 0;
}