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)

N = int(input())
A = [int(input()) for i in range(N)]

A.sort()

max_list = []
i = 0
if len(A) % 2 == 1:
    if abs(A[-1] - A[int(len(A)/2)]) > abs(A[0] - A[int(len(A)/2)]):
        max_list.append(A.pop(int(len(A)/2)))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop())
            else:
                max_list.append(A.pop(0))
            i += 1
            if len(A) ==0:
                break
    else:
        max_list.append(A.pop(int(len(A)/2)))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop(0))
            else:
                max_list.append(A.pop())
            i += 1
            if len(A) ==0:
                break

else:
    p1, p2, p3, p4 = abs(A[-1] - A[int(len(A)/2)]), abs(A[0] - A[int(len(A)/2)]), \
                     abs(A[-1] - A[int(len(A) / 2) - 1]), abs(A[0] - A[int(len(A) / 2) - 1])
    maxx = 0
    target = 0
    for y, x in enumerate([p1, p2, p3, p4]):
        if x > maxx:
            maxx = x
            target = y

    if y == 0:
        max_list.append(A.pop(int(len(A)/2)))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop(0))
            else:
                max_list.append(A.pop())
            i += 1
            if len(A) == 0:
                break
    elif y == 1:
        max_list.append(A.pop(int(len(A)/2)))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop())
            else:
                max_list.append(A.pop(0))
            i += 1
            if len(A) == 0:
                break

    if y == 2:
        max_list.append(A.pop(int(len(A)/2)-1))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop(0))
            else:
                max_list.append(A.pop())
            i += 1
            if len(A) ==0:
                break
    if y == 3:
        max_list.append(A.pop(int(len(A)/2)-1))
        while True:
            if i % 2 == 0:
                max_list.append(A.pop())
            else:
                max_list.append(A.pop(0))
            i += 1
            if len(A) == 0:
                break

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

print(ans)