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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Split(' ');
            int jcount = int.Parse(line[0]);

            //価値、コスト
            var pairs = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).Zip(Console.ReadLine().Split(' ').Select(c => int.Parse(c)), (v, c) => new KeyValuePair<int, int>(v, c)).ToList();

            var perms = Permutation<int>.All(Enumerable.Range(0, pairs.Count)).ToList();

            int delta = 0;
            int cx = 0, cy = 0;
            foreach (var indexes in perms)
            {
                foreach (var i in indexes)
                {
                    cx += pairs[i].Key;
                    cy += pairs[i].Value;

                    if (cx - cy > delta)
                    {
                        delta = cx - cy;
                    }
                }

                cx = 0;
                cy = 0;
            }

            Console.WriteLine(Math.Max(0, delta));
        }

        static class Permutation<T>
        {
            private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
            {
                int N = a.Length;
                if (N == 0)
                {
                    perms.Add(stack.Reverse().ToArray());
                }
                else
                {
                    var b = new T[N - 1];
                    Array.Copy(a, 1, b, 0, N - 1);
                    for (int i = 0; i < a.Length; ++i)
                    {
                        stack.Push(a[i]);
                        Search(perms, stack, b);
                        if (i < b.Length) { b[i] = a[i]; }
                        stack.Pop();
                    }
                }
            }
            public static IEnumerable<T[]> All(IEnumerable<T> src)
            {
                var perms = new List<T[]>();
                Search(perms, new Stack<T>(), src.ToArray());
                return perms;
            }
        }
    }
}