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
happy = gets.split.map(&:to_i)
happy.unshift 0 # ダミー

# 貪欲法
# happyが多い順にインデックスを並び替える
sorted_index = (1..n).sort_by{|i| -happy[i]}

total = 0
first = 1
last = n
sorted_index.each do |i|
  first_dist = (i - first).abs
  last_dist = (last - i).abs
  if first_dist > last_dist
    total += happy[i] * first_dist
    first += 1
  else
    total += happy[i] * last_dist
    last -= 1
  end
end

puts total