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: Accepted)

import sys
from collections import deque

input = sys.stdin.readline


def main():
    N = int(input())
    A = [0] * N
    for i in range(N):
        A[i] = int(input())

    A.sort()
    ans = 0
    if N % 2 == 1:
        # center is minimum
        a = deque(A[1:])
        b = deque([A[0]])
        nxt = "r"
        while a:
            if nxt == "r":
                nxt = "l"
                x = a.pop()
                y = a.pop()
                b.appendleft(x)
                b.append(y)
            else:
                nxt = "r"
                x = a.popleft()
                y = a.popleft()
                b.appendleft(x)
                b.append(y)
        diff = sum(abs(b[i + 1] - b[i]) for i in range(N - 1))
        ans = max(ans, diff)
        # center is maximum
        a = deque(A[::-1][1:])
        b = deque([A[-1]])
        nxt = "r"
        while a:
            if nxt == "r":
                nxt = "l"
                x = a.pop()
                y = a.pop()
                b.appendleft(x)
                b.append(y)
            else:
                nxt = "r"
                x = a.popleft()
                y = a.popleft()
                b.appendleft(x)
                b.append(y)
        diff = sum(abs(b[i + 1] - b[i]) for i in range(N - 1))
        ans = max(ans, diff)

    else:
        # center is minimum
        a = deque(A[1:])
        b = deque([A[0]])
        nxt = "r"
        while a:
            if len(a) == 1:
                rem = a.pop()
                break
            if nxt == "r":
                nxt = "l"
                x = a.pop()
                y = a.pop()
                b.appendleft(x)
                b.append(y)
            else:
                nxt = "r"
                x = a.popleft()
                y = a.popleft()
                b.appendleft(x)
                b.append(y)
        diff = sum(abs(b[i + 1] - b[i]) for i in range(N - 2))
        diff += max(abs(rem - b[0]), abs(rem - b[-1]))
        ans = max(ans, diff)

        # center is maximum
        a = deque(A[::-1][1:])
        b = deque([A[-1]])
        nxt = "r"
        while a:
            if len(a) == 1:
                rem = a.pop()
                break
            if nxt == "r":
                nxt = "l"
                x = a.pop()
                y = a.pop()
                b.appendleft(x)
                b.append(y)
            else:
                nxt = "r"
                x = a.popleft()
                y = a.popleft()
                b.appendleft(x)
                b.append(y)
        diff = sum(abs(b[i + 1] - b[i]) for i in range(N - 2))
        diff += max(abs(rem - b[0]), abs(rem - b[-1]))
        ans = max(ans, diff)

    print(ans)


if __name__ == "__main__":
    main()