Problem:
Score : 500 points

Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

Constraints

2 \leq N \leq 2000

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_2 ... A_N

Output

Print the maximum total happiness points the children can earn.

Sample Input 1

4
1 3 4 2

Sample Output 1

20

If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

Sample Input 2

6
5 5 6 1 1 1

Sample Output 2

58

Sample Input 3

6
8 6 9 1 2 1

Sample Output 3

85

Solution in C# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Collections.Generic;
namespace AtCoder
{
    class Abc162F
    {

        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());

            var a = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            Array.Sort(a);
            Array.Reverse(a);

            long max = 0;
            int i = 0, j = n;
            while(i<j)
            {
                max = max + a[i] * (Math.Abs(j - (i+1))) + a[j-1] * (Math.Abs(j - (i+1)));
                i++;
                j--;
            }

            Console.Write(max);
            Console.WriteLine();

        }
    }
}