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 (3.8.2) (judge verdict: Wrong Answer)

from collections import deque
import sys
input = sys.stdin.readline
n = int(input())
As = sorted([int(input()) for i in range(n)])
q = deque(As[1:])
ans = 0
cnt = 1
# 初期化
p1 = As[0]
p2 = As[0]
flg = False
while True:
    if len(q) == 0: break
    if flg:
        n1 = q.popleft()
    else:
        n1 = q.pop()
    ans += abs(p1-n1)
    p1 = n1

    if len(q) == 0: break
    if flg:
        n2 = q.popleft()
    else:
        n2 = q.pop()
    ans += abs(p2-n2)
    p2 = n2

    flg = not flg

print(ans)