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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
const INPUT_DELIMITER = " ";
const OUTPUT_DELIMITER = " ";

$input1 = fgets(STDIN);
$input2 = fgets(STDIN);
$inputArray = explode(INPUT_DELIMITER, $input2);

$count = 0;
foreach ($inputArray as $index => $input) {
    if ($input >= $input1) {
        continue;
    }
    if (!isset($inputArray[$index-1]) || !isset($inputArray[$index+1])) {
        continue;
    }
    $array = [$inputArray[$index-1], $input,$inputArray[$index+1]];
    sort($array);
    if ($array[1] == $input) {
        $count++;
    }
}

echo $count;