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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $N);
$a = [];
$ans = 0;
for ($i = 0; $i < $N; $i++) {
    fscanf(STDIN, "%d", $a[]);
}
sort($a);
$b = $a;

//Lowから
$low = array_splice($a, 0, ceil($N / 2));
rsort($a);
$high = $a;

$tmp = 0;
for ($i = 0; $i < count($high); $i++) {
    if ($i === 0) {
        $tmp += abs($low[0] - $high[0]);
    } else {
        $tmp += abs($low[$i - 1] - $high[$i]);
    }
}
for ($i = 1; $i < count($low); $i++) {
    $tmp += abs($high[$i - 1] - $low[$i]);
}
$score1 = $tmp;

rsort($b);
//highから
$high = array_splice($b, 0, ceil($N / 2));
sort($b);
$low = $b;

$tmp = 0;
for ($i = 0; $i < count($low); $i++) {
    if ($i === 0) {
        $tmp += abs($high[0] - $low[0]);
    } else {
        $tmp += abs($high[$i - 1] - $low[$i]);
    }
}
for ($i = 1; $i < count($high); $i++) {
    $tmp += abs($low[$i - 1] - $high[$i]);
}
$score2 = $tmp;

printf("%d", max($score1, $score2));