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 #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE Strict #-}
import Data.Char (isSpace)
import Data.Int (Int64)
import Data.Array.Unboxed
import Data.Array.ST
import Control.Monad
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import qualified Data.ByteString.Char8 as BS
import Data.Bits
import qualified Data.Sequence as Seq
import Data.Semigroup

maxUreshisa :: Int -> Seq.Seq (Int, Int64) -> (Int64, Int)
maxUreshisa j seq = getMax $ Seq.foldMapWithIndex (\index (i, a) -> Max (a * fromIntegral (abs (i - j)), index)) seq

main = do
  n <- readLn @Int
  xs <- U.map fromIntegral . U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let loop :: Int -> Int -> Int64 -> Seq.Seq (Int, Int64) -> Int64
      loop k l acc ys | k == l = acc
                      | otherwise = let (left, leftIndex) = maxUreshisa k ys
                                        (right, rightIndex) = maxUreshisa (l - 1) ys
                                    in if left > right
                                       then loop (k + 1) l (acc + left) (Seq.deleteAt leftIndex ys)
                                       else loop k (l - 1) (acc + right) (Seq.deleteAt rightIndex ys)
  print $ loop 0 n 0 (Seq.fromList $ U.toList $ U.indexed xs)