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: Accepted)

console.log(main(require("fs").readFileSync("/dev/stdin","utf8")));
function main(inp){
  inp = inp.split("\n").map(a=>+a);
  var n = inp[0];
  var s = [];
  for(var i = 0; i < n; i++)s[i] = inp[i+1];
  s.sort((a,b)=>a-b);
  var ans = 0;
  var m = n + 1 >> 1;
  for(i = 0; i < m; i++){
    ans -= s[i] * 2;
  }
  for(; i < n; i++){
    ans += s[i] * 2;
  }
  if(n % 2 === 0)return ans - s[m] + s[m-1];
  if(s[m-1]+s[m-2] > s[m-1]*3-s[m])return ans + s[m-1] + s[m-2];
  else return ans + s[m-1]*3 - s[m];
}