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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Abc163E
    {
        struct Baby
        {
            public int Index;
            public long Value;
            public Baby(int index, long value)
            {
                Index = index;
                Value = value;
            }
        }

        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split(' ').Select((s, i) => new Baby(i, long.Parse(s))).OrderByDescending(i => i.Value).ToArray();

            var dp = new long[n + 1, n + 1];


            for (int i = 0; i < n; i++)
            {
                for (int l = 0; l <= i; l++)
                {
                    var r = i - l;
                    dp[l + 1, r] = Math.Max(dp[l + 1, r], dp[l, r] + a[i].Value * Math.Abs(a[i].Index - l));
                    dp[l, r + 1] = Math.Max(dp[l, r + 1], dp[l, r] + a[i].Value * Math.Abs(a[i].Index - (n - 1 - r)));
                }
            }

            long max = 0;
            for (int i = 0; i <= n; i++)
                if (max < dp[i, n - i])
                    max = dp[i, n - i];
            Console.WriteLine(max);
        }
    }
}