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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp1
{
    internal class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var Vs = Console.ReadLine().Split(' ').Select(x=>int.Parse(x)).ToArray();
            var Cs = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var i = 1;
            var max = 0;
            while (i <= N)
            {
                var vs = Comb(Vs, i);
                var cs = Comb(Cs, i);
                var tmp = vs.Zip(cs, (x, y) => x.Sum() - y.Sum()).Max();
                if(tmp > max)
                {
                    max = tmp;
                }
                i ++;
            }
            Console.WriteLine(max);
        }
        static IEnumerable<IEnumerable<T>> Comb<T>(IEnumerable<T> items, int r)
        {
            if (r == 0)
            {
                yield return Enumerable.Empty<T>();
            }
            else
            {
                var i = 1;
                foreach (var x in items)
                {
                    var xs = items.Skip(i);
                    foreach (var c in Comb(xs, r - 1))
                        yield return Before(c,x);

                    i++;
                }
            }
        }
        static IEnumerable<T> Before<T>(IEnumerable<T> items, T first)
        {
            yield return first;

            foreach (var i in items)
                yield return i;
        }
    }
}