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)

import sys
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

from collections import deque

n = ni()
a = [ni() for _ in range(n)]
a.sort()

a = deque(a)
ans = deque([])

cur = a.popleft()
ans.append(cur)

cnt = 0
while len(a) > 1:
    if cnt%2 == 0:
        cur1 = a.pop()
        cur2 = a.pop()

    else:
        cur1 = a.popleft()
        cur2 = a.popleft()

    ans.append(cur1)
    ans.appendleft(cur2)
    cnt += 1

if len(a) == 1:
    if abs(a[0] - ans[0]) > abs(a[0] - ans[-1]):
        ans.appendleft(a[0])
    else:
        ans.append(a[0])

if len(a)%2:
    cur = a.popleft()
    ans.append(cur)

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

print(ret)