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 Pascal (FPC 2.6.2) (judge verdict: Time Limit Exceeded)

var n,i:integer;
a:array[0..100000]of longint;
f:array[1..100000]of 0..1;
tot:int64;
procedure s(x:integer;la:longint;ss:int64);
var j:integer;
begin 
	if x>n then begin if ss>tot then tot:=ss;exit;end;
	for j:=1 to n do 
	begin 
		if f[j]=0 then 
		begin 
			f[j]:=1;
			if x=1 then s(x+1,j,ss)
			else 
			s(x+1,j,ss+abs(a[j]-a[la]));
			f[j]:=0;
		end;
	end;
end;
begin 
	read(n);
	tot:=0;
	fillchar(f,sizeof(f),0);
	for i:=1 to n do read(a[i]);
	s(1,0,0);
	writeln(tot);
end.