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 Ruby (2.7.1) (judge verdict: Wrong Answer)

n = gets.to_i
as = gets.split(" ").map(&:to_i)

min_index = 0
max_index = n - 1

result = 0
n.times do
  potentials = as.map.with_index do |v, i|
    if i - min_index == max_index - i
      [v * (max_index - i), i, :horyu]
    elsif i - min_index < max_index - i
      [v * (max_index - i), i, max_index]
    else
      [v * (i - min_index), i, min_index]
    end
  end

  max = potentials.max{|a, b| a[0] <=> b[0]}
  result += max[0]
  as[max[1]] = 0
  
  min_index += 1 if min_index == max[2]
  max_index -= 1 if max_index == max[2]
end

puts result