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: Accepted)

from collections import deque

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

A.sort()

X = deque(A.copy())

B = deque([X.pop()])
flg = True
while X:
    if flg:
        B.append(X.popleft())
        if X:
            B.appendleft(X.popleft())
    else:
        B.append(X.pop())
        if X:
            B.appendleft(X.pop())
    flg = not flg

X = deque(A.copy())
C = deque([X.popleft()])
flg = True
while X:
    if flg:
        C.append(X.pop())
        if X:
            C.appendleft(X.pop())
    else:
        C.append(X.popleft())
        if X:
            C.appendleft(X.popleft())
    flg = not flg

print(max(sum([abs(B[i]-B[i-1]) for i in range(1,N)]), sum([abs(C[i]-C[i-1]) for i in range(1,N)])))