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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$n = trim(fgets(STDIN));
$p = explode(" ", fgets(STDIN));
$count = 0;

for ($i = 0; $i < $n - 2; $i++) {
  $three  = array($p[$i], $p[$i+1], $p[$i+2]);
  if (!isUniqueArray($three)) continue;
  $_three = $three;
  sort($_three);
  if ($three[1] == $_three[1]) $count++;
}
echo $count,PHP_EOL;

// 配列内の全ての値が一意かチェックする
function isUniqueArray ($target_array) {
  $unique_array = array_unique($target_array);
  if (count($unique_array) === count($target_array)) {
    return true;
  }
  else {
    return false;
  }
}