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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE TypeApplications #-}
import Data.Char (isSpace)
import Data.Int (Int64)
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Algorithms.Merge as A
import qualified Data.ByteString.Char8 as BS

solveL :: Int -> U.Vector (Int, Int64) -> Int64
solveL n xs = let ys = U.modify (A.sortBy (\(i,a) (j,b) -> compare b a <> compare i j)) xs
              in sum [ fromIntegral (abs (n - 1 - i - j)) * a | (i,(j,a)) <- zip [0..] (U.toList ys) ]

solveR :: U.Vector (Int, Int64) -> Int64
solveR xs = let ys = U.modify (A.sortBy (\(i,a) (j,b) -> compare b a <> compare i j)) xs
            in sum [ fromIntegral (abs (j - i)) * a | (i,(j,a)) <- zip [0..] (U.toList ys) ]

solve :: Int -> U.Vector Int64 -> Int64
solve m xs = let (xs0, xs1) = U.splitAt m (U.indexed xs)
             in solveL (U.length xs) xs0 + solveR xs1

main = do
  n <- readLn @Int
  xs <- U.map fromIntegral . U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  print $ maximum [ solve i xs | i <- [1..n-1] ]