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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Text;
using System.Linq;
using static System.Math;

class Program{
	static int n;
	static int[] a;

	static void Main(){
		/* 入力の受取, aのソート */
		n = int.Parse(Console.ReadLine());
		a = new int[n];
		for (int i = 0;i < n;i++) a[i] = int.Parse(Console.ReadLine());
		Array.Sort(a);

		long ans = 0;
		/* \/\/\/... */
		int[] count = new int[n];
		bool f = true; //trueで\,falseで/
		for (int i = 0;i < n - 1;i++){
			if (f){
				count[i]++;
				count[i+1]--;
				goto END;
			}
			count[i]--;
			count[i+1]++;
			END:
			f = !f;
		}
		Array.Sort(count);
		long temp = 0;
		for (int i = 0;i < n;i++)
			temp += count[i] * a[i];
		ans = Max(ans,temp);
		/* /\/\/\/... */
		count = new int[n];
		f = false;
		for (int i = 0;i < n - 1;i++){
			if (f){
				count[i]++;
				count[i+1]--;
				goto END;
			}
			count[i]--;
			count[i+1]++;
			END:
			f = !f;
		}
		Array.Sort(count);
		temp = 0;
		for (int i = 0;i < n;i++)
			temp += count[i] * a[i];
		ans = Max(ans,temp);

		/* 出力 */
		Console.WriteLine(ans);
	}
}