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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

// MainT1P2018D
public class Main {

	public static void main(String[] args) {
		try (Scanner in = new Scanner(System.in)) {
			final int N = in.nextInt();
			int d = 8*N + 1;
			int dr = (int)Math.sqrt(d);
			if (dr * dr != d) {
				System.out.println("No");
				return;
			}

			final int k = (1 + dr) / 2;

			final int[] startIdx = new int[k - 1];
			{
				int idx = 1;
				for (int i = 0; i < k - 1; ++i) {
					startIdx[i] = idx;
					idx += i + 1;
				}
			}

			System.out.println("Yes");
			System.out.println(k);
			{
				System.out.print(k - 1);
				for (int i = 0; i < k - 1; ++i) {
					System.out.print(' ');
					System.out.print(startIdx[i] + i);
				}
				System.out.println();
			}
			for (int i = 0; i < k - 1; ++i) {
				System.out.print(k - 1);
				for (int j = 0; j < i; ++j) {
					System.out.print(' ');
					System.out.print(startIdx[i] + j);
				}
				for (int j = i; j < k - 1; ++j) {
					System.out.print(' ');
					System.out.print(startIdx[j] + i);
				}
				System.out.println();
			}
		}
	}
}