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: Accepted)

N = gets.to_i
A = gets.chomp.split.map(&:to_i)

A = A.map.with_index { |elem, index| [index, elem]}
A = A.sort_by { |a| a[1] }.reverse

dpnxy = [[0,0]]
dpnxy1 = []
dpn = [0]
dpn1 = []

(1..N).each do |n|
  (0..(dpnxy.length-1)).each do |i|
    x = dpnxy[i][0]
    y = dpnxy[i][1]
    n_left = x
    n_right = N-1-y

    if A[n-1][0] >= n_left
      l = dpn[i] + A[n-1][1] * (A[n-1][0] - n_left)
      
      if i!=0 and dpnxy1[dpnxy1.length-1][0] == x+1 and dpnxy1[dpnxy1.length()-1][1] == y
        if dpn1[dpn1.length-1] < l
          dpn1[dpn1.length-1] = l
        end
      else
        dpnxy1 << [x+1,y]
        dpn1 << l
      end
    end

    if A[n-1][0] <= n_right
      r = dpn[i] + A[n-1][1] * (n_right - A[n-1][0])
      dpnxy1 << [x,y+1]
      dpn1 << r
    end
  end
  dpnxy = dpnxy1
  dpn = dpn1
  dpnxy1 = []
  dpn1 = []
end
p dpn.max