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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n")
local a = {}
for i = 1, n do a[i] = io.read("*n") end
table.sort(a)

if n % 2 == 0 then
  local sum = 0
  local half = n / 2
  for i = 1, half do
    sum = sum - a[i] + a[half + i]
  end
  sum = sum * 2 - a[half + 1] + a[half]
  print(sum)
else
  local sum = 0
  local half = (n - 1) / 2
  for i = 1, half do
    sum = sum - a[i]
  end
  for i = half + 1, n do
    sum = sum + a[i]
  end
  sum = sum * 2 - a[half + 1] - a[half + 2]
  local cand = sum
  sum = 0
  half = (n + 1) / 2
  for i = 1, half do
    sum = sum - a[i]
  end
  for i = half + 1, n do
    sum = sum + a[i]
  end
  sum = sum * 2 + a[half - 1] + a[half]
  print(math.max(cand, sum))
end