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: Accepted)

<?php

fscanf(STDIN, "%d", $n);
$input = trim(fgets(STDIN));
$p_arr = explode(' ', $input);


$count = 0;
$tmp1 = $p_arr[0];
$tmp2 = $p_arr[1];
for ($i = 2; $i < $n; ++$i) {
    if (($tmp2 > $tmp1 && $tmp2 < $p_arr[$i]) || ($tmp2 < $tmp1 && $tmp2 > $p_arr[$i])) {
        ++$count;
    }

    $tmp1 = $tmp2;
    $tmp2 = $p_arr[$i];
}
echo $count;