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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <set>
#include <iomanip>
using namespace std;
int main() {
	long long n, k[100005], ans;
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> k[i];
	}
	sort(k, k + n);
	int a = 0, b = n - 1, aa, bb;
	ans = k[n - 1] - k[0];
	while (a < b) {
		aa = a + 1;
		bb = b - 1;
		if (aa == bb) {
			if (k[b] - k[aa] > k[bb] - k[a]) {
				ans += k[b] - k[aa];
				a = aa;
			}
			else {
				ans += k[bb] - k[a];
				b = bb;
			}
		}
		else {
			ans += k[b] - k[aa], ans += k[bb] - k[a];
			a = aa;
			b = bb;
		}
	}
	cout << ans << endl;
}