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;

class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var ai = a.Select((t, i) => new { Value = t, Index = i }).OrderByDescending(t => t.Value).ToArray();

        var isMoved = new bool[n];

        long sum = 0;

        // 活性度の高いのものから貪欲法
        for(int i = 0; i < n; i++)
        {
            var index = ai[i].Index;
            if (isMoved[index]) continue;

            long left = 0;
            long right = n - 1;
            for(int j = 0; j < index; j++)
            {
                if (isMoved[j] == false)
                {
                    left = j;
                    break;
                }
            }
            for(int j = n - 1; j > index; j--)
            {
                if (isMoved[j] == false)
                {
                    right = j;
                    break;
                }
            }

            long target = Math.Abs(index - left) > Math.Abs(right - index) ? left : right;
            isMoved[target] = true;
            isMoved[index] = true;
            var dis = Math.Abs(index - target);
            sum = sum + (a[index] * dis) + (a[target] * dis);
        }

        Console.WriteLine(sum);
    }

}