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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";
function Main(input) {
    let lines = input.split("\n").map((v) => v - 0);
    let N = lines.shift();
    let nums = new Array(N);
    for (let n = 0; n < N; n++) nums[n] = lines.shift();
    nums.sort((a, b) => a - b);
    const even = N % 2 == 0;
    const H = Math.ceil(N / 2);
    let ans = 0;
    if (even) {
        for (let n = 0, m = N - 1; n < H; n++, m--) {
            if (n < H - 1) {
                ans -= nums[n] * 2;
                ans += nums[m] * 2;
            } else {
                ans -= nums[n];
                ans += nums[m];
            }
        }
    } else if (N == 3) {
ans = nums[1]  - nums[0] * 2 + nums[2]; 
} else {
        for (let n = H; n < N; n++) ans += nums[n] * 2;
        ans -= (nums[H - 1] + nums[H - 2]);
        for (let n = 0; n < H - 2; n++) ans -= nums[n] * 2;
    }
    console.log(ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));