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;

class E
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Console.ReadLine().Split().Select(long.Parse).ToArray();

		var sum = 0L;
		var u = new bool[n];
		int l = 0, r = n - 1;

		while (l <= r)
		{
			int li = 0, ri = 0;
			long lv = -1, rv = -1;
			for (int i = 0; i < n; i++)
			{
				if (u[i]) continue;
				var v = a[i] * Math.Abs(i - l);
				if (lv <= v)
				{
					li = i;
					lv = v;
				}
				v = a[i] * Math.Abs(i - r);
				if (rv < v)
				{
					ri = i;
					rv = v;
				}
			}

			if (lv > rv)
			{
				sum += lv;
				u[li] = true;
				l++;
			}
			else if (lv < rv)
			{
				sum += rv;
				u[ri] = true;
				r--;
			}
			else
			{
				if (Math.Abs(li - l) >= Math.Abs(ri - r))
				{
					sum += lv;
					u[li] = true;
					l++;
				}
				else
				{
					sum += rv;
					u[ri] = true;
					r--;
				}
			}
		}

		Console.WriteLine(sum);
	}
}