Problem:
Score : 400 points

Problem Statement

You are given N integers; the i-th of them is A_i.
Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Sample Input 1

5
6
8
1
2
3

Sample Output 1

21

When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9

Sample Output 2

25

Sample Input 3

3
5
5
1

Sample Output 3

8

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
list($n) = ints();
for ($i = 0; $i < $n; ++$i) list($a[]) = ints();
$_a = $a;
rsort($a);
sort($_a);
for ($i = 0; $i < intdiv($n, 2); ++$i) {
    if ($i % 2 === 0) {
        $r[] = $_a[$i];
        $l[] = $a[$i];
    } else {
        $r[] = $a[$i];
        $l[] = $_a[$i];
    }
}
if ($n % 2) {
    if ($i % 2) $r[] = $a[$i];
    else $r[] = $_a[$i];
}
$aa = array_merge(array_reverse($l), $r);
$ans = 0;
for ($i = 0; $i < $n - 1; ++$i)
    $ans += abs($aa[$i + 1] - $aa[$i]);
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}