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)

def max(a,b); a > b ? a : b; end

Child = Struct.new(:value, :pos)
N = gets.to_i
A = gets.split.map(&:to_i).each_with_index.map{|a,i| Child.new(a, i + 1) }.sort_by(&:value).reverse
dp = Array.new(N + 1){ Array.new(N + 1, 0) }

ans = 0
A.each.with_index(1) do |c, n|
  x = c.pos
  v = c.value
  
  # padding all from left
  dp[n][0] = dp[n - 1][0] + v * (n - x).abs

  # padding all from right
  dp[0][n] = dp[0][n - 1] + v * (N + 1 - n - x).abs

  (1 ... n).each do |l|
    r = n - l
    dp[l][r] = max(dp[l][r - 1] + v * (N + 1 - r - x).abs, dp[l - 1][r] + v * (l - x).abs)
    ans = max(ans, dp[l][r])
  end
end
puts ans