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 Python (3.4.3) (judge verdict: Wrong Answer)

all_num = int(input())
nums = []
for i in range(all_num):
    nums.append( int(input()) )
	
nums = sorted(nums)

sort_nums = []
loop_num = int(all_num/2)
for i in range( loop_num ):
    if i % 2 == 0:
        sort_nums.append(nums[i])
        sort_nums.insert(0,nums[-(i+1)])
    else:
        sort_nums.insert(0,nums[i])
        sort_nums.append(nums[-(i+1)])
    
if len( nums ) % 2 == 1:
    if loop_num % 2 == 1:
        center_index = int(len(nums)/2)
        sort_nums.append(nums[center_index])
    else :
        center_index = int(len(nums)/2)
        sort_nums.insert(0,nums[center_index])


total = 0
for i in range( len(sort_nums)-1 ):
    total = total + abs(sort_nums[i] - sort_nums[i+1])

print( sort_nums )
print(total)