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 C (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

#define MAX(a, b) ((a) > (b) ? (a) : (b))

int INP[100000];

void quick_sort(int A[], int n){
    if (n > 1) {
        int h, i, j, pivot, tmp;
        pivot = A[0];
        for (h = i = j = 1; i < n; i++) {
            if (A[i] < pivot) {
                tmp = A[j];
                A[j] = A[i];
                A[i] = tmp;
                j++;
            } else if (A[i] == pivot) {
                A[i] = A[j];
                A[j] = A[h];
                h++;
                j++;
            }
        }
        for (i = 0; i < h; i++) {
            A[i] = A[j - i - 1];
            A[j - i - 1] = pivot;
        }
        quick_sort(A, j - h);
        quick_sort(A + j, n - j);
    }
}


int itr(int sp, int lp, int left, int right) {
    if (lp - sp < 0) return 0;

    int lc, islL = 0, rc, isrL = 0, abl, abr, tmpl, tmpr;

    if (left < INP[lp]) {
        lc = INP[lp];
        islL = 1;
    } else {
        lc = INP[sp];
    }
    if (right < INP[lp]) {
        rc = INP[lp];
        isrL = 1;
    } else {
        rc = INP[sp];
    }

    abl = abs(left - lc);
    abr = abs(right - rc);

    if (abl > abr) {
        if (islL) lp--;else sp++;
        return itr(sp, lp, lc, right) + abl;
    } else if (abl < abr) {
        if (isrL) lp--; else sp++;
        return itr(sp, lp, left, rc) + abr;
    }
    if (islL) lp--;else sp++;
    tmpl = itr(sp, lp, lc, right);
    if (islL) lp++;else sp--;
    if (isrL) lp--; else sp++;
    tmpr = itr(sp, lp, left, rc);
    return MAX(tmpl, tmpr) + abr;
}


int main() {
    int i, n, res = 0;

    scanf("%d", &n);
    for (i = 0; i < n; i++) scanf("%d", INP+i);
    quick_sort(INP, n);
    
    res = INP[n-1] - INP[0] + itr(1, n - 2, INP[n-1], INP[0]);
    
    printf("%d\n", res);
    return 0;
}