Problem:
Score : 500 points

Problem Statement

For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:

Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.

Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.

There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
C_1 C_2 \cdots C_N

Output

Print the sum of f(S, T), modulo (10^9+7).

Sample Input 1

1
1000000000

Sample Output 1

999999993

There are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:

S = (0), T = (1): by changing S_1 to 1, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.

S = (1), T = (0): by changing S_1 to 0, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.

The sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.

Sample Input 2

2
5 8

Sample Output 2

124

There are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:

S = (0, 1), T = (1, 0)

In this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is 5 \times 2 + 8 = 18. We cannot have S = T at a smaller cost, so f(S, T) = 18.

Sample Input 3

5
52 67 72 25 79

Sample Output 3

269312

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE ScopedTypeVariables #-}

import GHC.TypeLits
import Data.Int
import Data.Proxy
import qualified Data.Map.Lazy as Map
import Control.Monad
import Control.Monad.State
import Data.List

import Data.Maybe
import qualified Data.ByteString.Char8 as BS

import qualified Data.Vector.Unboxed as VU


getInts = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine


{-- Mod Int --}
data Mint (m :: Nat) = Mint {getMintValue :: Integer} deriving (Eq, Show)

getMintMod :: forall p. KnownNat p => Mint p -> Integer
getMintMod = natVal

makeMint :: forall p. KnownNat p => Integer -> Mint p
makeMint a = let r = Mint $ fromInteger $ a `mod` (getMintMod r) in r

instance KnownNat p => Num (Mint p) where
  (Mint a) + (Mint b) = makeMint $ a + b
  (Mint a) - (Mint b) = makeMint $ a - b
  (Mint a) * (Mint b) = makeMint $ a * b
  negate (Mint a) = makeMint $ negate a
  abs = id
  signum (Mint a) = if a == 0 then 0 else 1
  fromInteger = makeMint

invMint :: forall p. KnownNat p => Mint p -> Mint p
invMint m = let p = getMintMod m in m ^ (p - 2)

powerMint :: forall p. KnownNat p => Integer -> Integer -> Mint p
powerMint n p
  | p >= 0 = (fromInteger n :: Mint p) ^ p
  | otherwise = invMint $ powerMint n (-p)


type M = Mint 1000000007




main :: IO ()
main = do
  n <- readLn :: IO Int
  c <- VU.fromList . sort <$> getInts

  let a = (powerMint 2 (fromIntegral $ 2 * n - 2) :: M)

  let ans = (* a) $ sum [(fromIntegral $ i+1) * (fromIntegral $ c VU.! (fromIntegral $ n-i))| i <- [1..n]]
  
  print $ getMintValue ans

  return ()