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)

# https://atcoder.jp/contests/tenka1-2018-beginner/tasks/tenka1_2018_c
from collections import deque
n = int(input())
nums = []
for _ in range(n):
    nums.append(int(input()))
nums.sort()
ans = 0
l = 0
r = n - 1
q = deque()
while l <= r:
    left = nums[l]
    right = nums[r]
    if not q:
        ans += abs(right - left)
        q.append(left)
        q.append(right)
        l += 1
        r -= 1
    else:
        s = max(abs(q[-1] - right), abs(q[0] - right))
        t = max(abs(q[-1] - left), abs(q[0] - left))
        if s >= t:
            if abs(q[-1] - right) > abs(q[0] - right):
                ans += abs(q[-1] - right)
                q.append(right)
            else:
                ans += abs(q[0] - right)
                q.appendleft(right)
            r -= 1
        else:
            if abs(q[-1] - left) > abs(q[0] - left):
                ans += abs(q[-1] - left)
                q.append(left)
            else:
                ans += abs(q[0] - left)
                q.appendleft(left)
            l += 1
print(ans)