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 PyPy3 (2.4.0) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
"""
Created on Mon Apr 15 22:46:42 2019

@author: Yamazaki Kenichi
"""
import math
N = int(input())
A = [int(input()) for i in range(N)]

A.sort()

temp1,temp2 = 0,0
if N%2 != 55:
    temp1 += A[-1]+A[-2]-2*A[0]
#    print(temp1,A[-1],A[-2],A[0])
    for i in range(N//2-1):
        temp1 += A[-1-(math.ceil(i/2)*2)] - A[(i//2*2)+1]
        temp1 += A[-2-(math.ceil(i/2)*2)] - A[(i//2*2)+2]
#        print(temp1,-1-(math.ceil(i/2)*2),-2-(math.ceil(i/2)*2),(i//2*2)+1,(i//2*2)+2)
    temp2 += 2*A[-1]-A[0]-A[1]
#    print(temp2,A[-1],A[0],A[1])
    for i in range(N//2-1):
        temp2 += A[-2-(i//2*2)] - A[(math.ceil(i/2)*2)]
        temp2 += A[-3-(i//2*2)] - A[(math.ceil(i/2)*2)+1]
#        print(temp2,-2-(i//2*2),-3-(i//2*2),(math.ceil(i/2)*2),(math.ceil(i/2)*2))
print(max(temp1,temp2))