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
A = gets.chomp.split.map(&:to_i)
left = 0
right = N-1
result = 0

B = A.map.with_index { |elem, index| [elem, index]}
C = B.each do |b|
  b << [b[0] * (b[1]-left), b[0] * (right-b[1])].max
end
D = C.sort_by { |b| b[2] }.reverse
D.each do |d|
  if d[1] - left >= right - d[1]
    result += d[0] * (d[1]-left)
    left += 1
  else
    result += d[0] * (right - d[1])
    right -= 1
  end
end

p result