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.split(' ').map &:to_i

map = {}
a.each_with_index do |a, i|
 map[i+1] = a
end

sum = 0
l = 1
r = n
while !map.empty?
 pos = map.key(map.values.max)
 r_sum = (r - pos).abs
 l_sum = (pos - l).abs
 # puts [l, r, pos, a[pos-1], r_sum, l_sum, sum].inspect

 if r_sum >= l_sum
  sum += r_sum * a[pos-1]
  r -= 1
 else
  sum += l_sum * a[pos-1]
  l += 1
 end

 map.delete pos
end

puts sum