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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h> 
int sort1(int n1,int n2,int n3);
int main()
{
	int n,a[25],i,j,t,num=1,x[25],c=0;
	scanf("%d",&n);
	for(i=0;i<n;i++){
		scanf("%d",&a[i]);
	}
	for(i=0;i<=n-3;i++){
		x[i]=sort1(a[i],a[i+1],a[i+2])+i;
		c++;
	}
	for(i=1;i<c;i++){
		if(x[i]!=x[i-1])
			num++;
	}
	printf("%d",num);
	return 0;
}

int sort1(int n1,int n2,int n3){
	int n,flag=2;
	if(n1>n2){
		n=n1;
		n1=n2;
		n2=n;
		flag=1;
	}
	if(n2>n3){
		n=n2;
		n2=n3;
		n3=n;
		flag=3;
	}
	if(n1>n2){
		n=n1;
		n1=n2;
		n2=n;
		flag=2;
	}
	return flag;
}