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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

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

namespace AtCoder.E
{
    internal static class CR
    {
        public static string GetText() { return Console.ReadLine(); }
        public static List<string> GetTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long GetLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> GetLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }
    }

    public class Program
    {
        public static long N { get; private set; }
        public static List<long> A { get; private set; }

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            N = CR.GetLong();
            A = CR.GetLongs();

            var table = new List<Score>();
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    table.Add(new Score
                    {
                        Value = A[i] * Math.Abs(i - j),
                        X = i,
                        Y = j,
                    });
                }
            }

            table = table.OrderByDescending(x => x.Value).ToList();
            var sum = 0L;
            for (int i = 0; i < N; i++)
            {
                var max = table.First();
                sum += max.Value;
                table.RemoveAll(x => x.X == max.X || x.Y == max.Y);
            }

            return sum;
        }

        class Score
        {
            public long Value { get; set; }
            public long X { get; set; }
            public long Y { get; set; }
        }
    }
}