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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import sys
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline

def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N] = [long(input_raw[0])]
    A = []
    for i in range(N):
        input_raw = read_func().strip().split()
        A.append(long(input_raw[0]))

    A.sort()

    B = deque([])
    is_back = False
    for i in range(N):
        if len(B) == 0:
            B.append(A[i])
        else:
            if is_back == False:
                x = A[i/2]
            else:
                x = A[len(A) - 1 - i/2]

            if abs(B[0] - x) > abs(B[len(B) - 1] - x):
                B.appendleft(x)
            else:
                B.append(x)
        if is_back == False:
            is_back = True
        else:
            is_back = False
    score1 = 0L
    for i in range(N -1):
        score1 += abs(B[i] - B[i + 1])


    A.sort(reverse = True)

    B = deque([])
    is_back = False
    for i in range(N):
        if len(B) == 0:
            B.append(A[i])
        else:
            if is_back == False:
                x = A[i/2]
            else:
                x = A[len(A) - 1 - i/2]

            if abs(B[0] - x) >= abs(B[len(B) - 1] - x):
                B.appendleft(x)
            else:
                B.append(x)
        if is_back == False:
            is_back = True
        else:
            is_back = False
    score2 = 0L
    for i in range(N -1):
        score2 += abs(B[i] - B[i + 1])

    print max(score1, score2)


if __name__ == '__main__':
    main()