Problem:
Score : 200 points

Problem Statement

There are N gems. The value of the i-th gem is V_i.

You will choose some of these gems, possibly all or none, and get them.

However, you need to pay a cost of C_i to get the i-th gem.

Let X be the sum of the values of the gems obtained, and Y be the sum of the costs paid.

Find the maximum possible value of X-Y.

Constraints

All values in input are integers.

1 \leq N \leq 20

1 \leq C_i, V_i \leq 50

Input

Input is given from Standard Input in the following format:

N
V_1 V_2 ... V_N
C_1 C_2 ... C_N

Output

Print the maximum possible value of X-Y.

Sample Input 1

3
10 2 5
6 3 4

Sample Output 1

5

If we choose the first and third gems, X = 10 + 5 = 15 and Y = 6 + 4 = 10.
We have X-Y = 5 here, which is the maximum possible value.

Sample Input 2

4
13 21 6 19
11 30 6 15

Sample Output 2

6

Sample Input 3

1
1
50

Sample Output 3

0

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

import Control.Applicative
import Control.Monad
import Data.List
import Data.Array

main = do
  n <- (read::String -> Int) <$> getLine
  values <- array (1, n) . zip [1..n] . map (read::String -> Int) . words <$> getLine
  costs <- array (1, n) . zip [1..n] . map (read::String -> Int) . words <$> getLine
  let results = calc n values costs
  print $ maximum results
 

calc::Int -> Array Int Int -> Array Int Int -> [Int]
calc n values costs = do
  set <- filterM (const [True, False]) [1..n]
  let vsum = foldl (\acc i -> acc + values ! i) 0 set
      csum = foldl (\acc i -> acc + costs ! i) 0 set
  return $ vsum - csum