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: Accepted)

using System;
using System.Linq;
using System.Runtime.CompilerServices;
using CompLib.Util;

public class Program
{
    int N;
    long[] A;
    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        A = sc.LongArray();

        // A[i]が大きいやつはたくさん移動させたい

        // iまで見る、左埋まってる数-右+N
        var dp = new long[N + 1, 2 * N + 1];
        for (int i = 0; i <= N; i++)
        {
            for (int j = 0; j <= 2 * N; j++)
            {
                dp[i, j] = long.MinValue;
            }
        }

        dp[0, N] = 0;
        var sortedByA = new int[N];
        for (int i = 0; i < N; i++)
        {
            sortedByA[i] = i;
        }

        Array.Sort(sortedByA, (l, r) => A[r].CompareTo(A[l]));


        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j <= 2 * N; j++)
            {
                if (dp[i, j] == long.MinValue) continue;
                int d = j - N;
                long l = (i + d) / 2;
                long r = i - l;

                // 左に移動
                dp[i + 1, j + 1] = Math.Max(dp[i + 1, j + 1], dp[i, j] + A[sortedByA[i]] * (sortedByA[i] - l));
                // 右に移動
                dp[i + 1, j - 1] = Math.Max(dp[i + 1, j - 1], dp[i, j] + A[sortedByA[i]] * (N - 1 - r - sortedByA[i]));
            }
        }

        long ans = long.MinValue;
        for (int i = 0; i <= 2 * N; i++)
        {
            ans = Math.Max(ans, dp[N, i]);
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}