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)

n = gets.to_i
value = gets.split(" ").map(&:to_i)
cost = gets.split(" ").map(&:to_i)

v_c = []
for i in 0..n-1
  array = [value[i], cost[i]]
  v_c << array
end

ans = []
for i in 1..2 ** n
  bit = i
  combi = []
  v_c.each_with_index do |v, j|
    if bit[j] == 1
      combi << v
    end
  end
  if !combi.empty?
    x = 0 ; y = 0
    combi.each do |com|
      x += com[0] ; y += com[1]
    end
    ans << x - y
  elsif combi.empty?
    ans << 0
  end
end

puts ans.max