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.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ForYellow
{
    class ABC_163
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            long[] array = ReadLongs();
            var remain = new HashSet<int>();
            for(int i = 0; i < n; i++)
            {
                remain.Add(i);
            }
            long res = 0;
            for(int i = 0; i < n; i++)
            {
                long[][] left = new long[i + 1][];
                long[][] right = new long[n - i - 1][];
                for(int j = 0; j <= i; j++)
                {
                    left[j] = new long[2] { array[j], j };
                }
                for(int j = i + 1; j < n; j++)
                {
                    right[j - i - 1] = new long[2] { array[j], j };
                }

                long tmp = 0;
                left = left.OrderBy(a => -a[0]).ToArray();
                right = right.OrderBy(a => -a[0]).ToArray();
                long l = 0;
                long r = n - i - 2;
                if (l <= r)
                {
                    for(int j = 0; j < n - i - 1; j++)
                    {
                        tmp += Abs(j - right[j][1]) * right[j][0];
                    }
                }
                l = n - i - 1;
                r = n - 1;
                for (int j = 0; j <= i; j++)
                {
                    tmp += Abs(n - 1 - j - left[j][1]) * left[j][0];
                }
                res = Max(res, tmp);
            }

            WriteLine(res);
        }

        static void DFS(HashSet<int> remain, List<int> used, ref long res,long[] vals)
        {
            if (remain.Count == 0)
            {
                long tmp = 0;
                for(int i = 0; i < used.Count; i++)
                {
                    tmp += Abs(used[i] - i) * vals[used[i]];
                }

                if (tmp > res)
                {
                    for(int i = 0; i < used.Count; i++)
                    {
                        Write(vals[used[i]] + " ");
                    }
                    WriteLine();
                    res = tmp;
                }
            }

            var next = new HashSet<int>();
            foreach(int idx in remain)
            {
                next.Add(idx);
            }

            foreach(int idx in remain)
            {
                used.Add(idx);
                next.Remove(idx);
                DFS(next, used, ref res, vals);
                used.RemoveAt(used.Count - 1);
                next.Add(idx);
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}