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()
{
	char inputa[6553500];
	char inputb[6553500];
	char numbuff[1000];
	int numbers[1000];
	int numnum;
	int match;

	fgets( inputa, 6553500, stdin );
	fgets( inputb, 6553500, stdin );
	if (strchr(inputa, '\n') != NULL) inputa[strlen(inputa) - 1] = '\0';
	if (strchr(inputb, '\n') != NULL) inputb[strlen(inputb) - 1] = '\0';

	numnum = 0;
	for( int i=0; inputb[i] !=0; i++ ) {
		if( inputb[i] == ' ' ) {
			continue;
		}
	
		int j=0;
		while( inputb[i] != 0 && inputb[i] != ' ' ) {
			numbuff[j++] = inputb[i++];
		}
		numbuff[j]=0;
		numbers[numnum++] = atoi(numbuff);

		if( inputb[i-1] == 0 ) {
			i--;
		}

	}

	match=0;
	for( int i =0; i < atoi(inputa) -2; i++ ) {
		if( numbers[i] < numbers[i+1] && numbers[i+1] < numbers[i+2]  ) {
			match++;
		}
	}

	printf("%d\n", match);
	return 0;

}