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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#! /usr/bin/env ruby

N = gets.chop.to_i
V = gets.chop.split.map(&:to_i).unshift(nil)
C = gets.chop.split.map(&:to_i).unshift(nil)

@choice_pattern_list = [[]]

def choice(i, choice_pattern)
  choice_pattern << i
  @choice_pattern_list << choice_pattern.dup
  bulk_choice(i+1, choice_pattern.dup)
end

def bulk_choice(start, choice_pattern)
  (start..N).to_a.each do |i|
    choice(i, choice_pattern.dup)
  end
end

bulk_choice(1, [])

result = @choice_pattern_list.map do |choice_pattern|
  choice_pattern.inject(0) do |sum, i|
    sum += V[i] - C[i]
  end
end << 0

p result.max