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 (7.3.0) (judge verdict: Wrong Answer)

N = int(input())
A = sorted([int(input()) for _ in range(N)])
if N%2==0:
    B = A[:N//2]
    C = A[N//2:]
    C = C[::-1]
    D1 = []
    D2 = []
    for i in range(N//2):
        D1.append(B[i])
        D1.append(C[i])
        D2.append(C[i])
        D2.append(B[i])
    cnt1 = 0
    cnt2 = 0
    for i in range(1,N):
        cnt1 += abs(D1[i]-D1[i-1])
        cnt2 += abs(D2[i]-D2[i-1])
    print(max(cnt1,cnt2))
else:
    B = A[:N//2]
    C = A[N//2+1:]
    C = C[::-1]
    D1 = []
    D2 = []
    for i in range(N//2):
        D1.append(B[i])
        D1.append(C[i])
        D2.append(C[i])
        D2.append(B[i])
    cnt1 = 0
    cnt2 = 0
    for i in range(1,N-1):
        cnt1 += abs(D1[i]-D1[i-1])
        cnt2 += abs(D2[i]-D2[i-1])
    cnt1 += max(A[N//2]-D1[0],D1[-1]-A[N//2])
    cnt2 += max(D2[0]-A[N//2],A[N//2]-D2[-1])
    print(max(cnt1,cnt2))