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;

namespace AtCoder.Problems
{
    public class ProblemE
    {
        public static void Main(string[] args)
        {
            var s = new SolveE();
            s.Solve();
        }

        public class Scanner
        {
            private string[] _s;
            private int _i;
            private readonly char[] _separators = new char[] { ' ' };

            public Scanner()
            {
                _s = new string[0];
                _i = 0;
            }

            public string Next()
            {
                if (_i < _s.Length) return _s[_i++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();
                _s = st.Split(_separators, StringSplitOptions.RemoveEmptyEntries);
                if (_s.Length == 0) return Next();
                _i = 0;
                return _s[_i++];
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public ulong NextULong() => ulong.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            public int[] GetIntArray(int n, int add = 0)
            {
                int[] array = new int[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextInt() + add;
                }
                return array;
            }

            public long[] GetLongArray(int n, long add = 0)
            {
                long[] array = new long[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextLong() + add;
                }
                return array;
            }

            public double[] GetDoubleArray(int n, double add = 0)
            {
                double[] array = new double[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextDouble() + add;
                }
                return array;
            }
        }
    }

    public class SolveE
    {
        public void Solve()
        {
            var cin = new ProblemE.Scanner();
            var n = cin.NextInt();
            var a = cin.GetIntArray(n);

            var result = GetAnswer(n, a);
            Console.WriteLine(result);
        }

        public long GetAnswer(int n, int[] a)
        {
            var answer = 0L;
            var left = 0;
            var right = n - 1;
            for (int i = 0; i < n; i++)
            {
                var isLeft = true;
                // Left
                var maxLeft = 0L;
                var maxLeftIndex = left;
                for (int y = 0; y < n; y++)
                {
                    var v = (long)a[y] * Math.Abs(left - y);
                    if (maxLeft < v || maxLeft == v && a[maxLeftIndex] > a[y])
                    {
                        maxLeft = v;
                        maxLeftIndex = y;
                    }
                }
                // Right
                var maxRight = 0L;
                var maxRightIndex = right;
                for (int y = 0; y < n; y++)
                {
                    var v = (long)a[y] * Math.Abs(right - y);
                    if (maxRight < v || maxRight == v && a[maxRightIndex] > a[y])
                    {
                        maxRight = v;
                        maxRightIndex = y;
                        isLeft = false;
                    }
                }

                if (maxLeftIndex == maxRightIndex)
                {
                    for (int j = 0; j <= n / 2; j++)
                    {
                        if (a[j] < a[n - 1 - j])
                        {
                            isLeft = true;
                            break;
                        }
                        if (a[j] > a[n - 1 - j])
                        {
                            isLeft = false;
                            break;
                        }
                    }
                }

                if (isLeft)
                {
                    answer += maxLeft;
                    a[maxLeftIndex] = 0;
                    left++;
                }
                else
                {
                    answer += maxRight;
                    a[maxRightIndex] = 0;
                    right--;
                }
            }
            return answer;
        }
    }
}