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: Runtime Error)

-- 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.List
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

main = do
  n <- readLn @Int
  xs <- U.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let arr :: UArray (Int,Int) Int64
      arr = runSTUArray do
        a <- newArray ((0,0),(n-1,n-1)) 0
        forM_ [0..n-1] \i -> do
          forM_ [0..n-1] \j -> do
            writeArray a (i,j) $! fromIntegral (xs U.! i) * fromIntegral (abs (i - j))
        return a
      v :: U.Vector Int64
      v = U.create do
        v <- UM.replicate (2^n) 0
        forM_ [0..n-1] \i -> do
          UM.write v (bit i) (arr ! (0,i))
        let f i = do
              a <- UM.read v i
              if a > 0
                then return a
                else do
                let loop m 0 = pure m
                    loop m k = do
                      let l = countTrailingZeros k
                          k' = clearBit i l
                          b = arr ! (popCount i - 1, l)
                      u <- f k'
                      loop (max m (b + u)) (clearBit k l)
                m <- loop 0 i
                UM.write v i m
                return m
        f (2^n-1)
        return v
  print $ U.last v