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 OCaml (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d" (fun n ->
    let a = Array.init n (fun _ -> Scanf.scanf " %d" (fun a -> a)) in
    Array.sort compare a;

    let rec check v1 v2 lp rp sum =
        if lp > rp then sum else
            let q = [| abs (v1 - a.(lp)), 0;
                       abs (v2 - a.(lp)), 1;
                       abs (v1 - a.(rp)), 2;
                       abs (v2 - a.(rp)), 3 |]
            in
            Array.sort compare q;
            match q.(3) with
            | v, 0 -> check a.(lp) v2     (lp + 1) rp       (sum + v)
            | v, 1 -> check v1     a.(lp) (lp + 1) rp       (sum + v)
            | v, 2 -> check a.(rp) v2     lp       (rp - 1) (sum + v)
            | v, _ -> check v1     a.(rp) lp       (rp - 1) (sum + v)
    in
    max (check a.(0) a.(0) 1 (n - 1) 0) (check a.(n - 1) a.(n - 1) 0 (n - 2) 0) |> Printf.printf "%d\n"
)