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;
using System.Text;
using System.Threading.Tasks;

namespace ABC20190427
{
    static class Program
    {
        static void Main(string[] args)
        {
            //Sample();
            //Biscuit();
            //Console.ReadLine();
            //Biscuit();
            //Console.ReadLine();
            //Biscuit();
            //Console.ReadLine();

            Resale();
            //Console.ReadLine();
            //Resale();
            //Console.ReadLine();

        }

        static void Biscuit()
        {
            // A B T
            string[] input = Console.ReadLine().Split(' ');
            int span = int.Parse(input[0]);
            int biscuitPerSpan = int.Parse(input[1]);
            int time = int.Parse(input[2]);

            int spanCount = time / span;
            int result = biscuitPerSpan * spanCount;
            
            //出力
            Console.WriteLine(result);
        }

        static void Resale()
        {
            // 整数の入力
            int n = int.Parse(Console.ReadLine());
            int[] jewelValues = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            int[] jewelCosts  = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();

            // 宝石オブジェクトに変換
            List<Jewel> jewelList = new List<Jewel>();
            for (int i = 0; i < n; i++)
            {
                jewelList.Add(new Jewel(jewelValues[i], jewelCosts[i]));
            }

            int result = 0;

            for (int i = 0; i < n; i++) {
                // 全ての組み合わせを試す。
                foreach (var ary in Comb(jewelList, i))
                {
                    int tmp = CalcProfit(ary);
                    if (result < tmp)
                    {
                        result = tmp;
                    }
                }
            }
            Console.WriteLine(result);
        }

        static int CalcProfit(IEnumerable<Jewel> jewelArray)
        {
            return jewelArray.Select(jewel => jewel.Value - jewel.Cost).Sum();
        }

        struct Jewel
        {
            public int Value { get; set; }
            public int Cost { get; set; }

            public Jewel(int value, int cost)
            {
                Value = value;
                Cost = cost;
            }
        }


        static void Sample()
        {
            // 整数の入力
            int a = int.Parse(Console.ReadLine());

            // スペース区切りの整数の入力
            string[] input = Console.ReadLine().Split(' ');
            int b = int.Parse(input[0]);
            int c = int.Parse(input[1]);

            // 文字列の入力
            string s = Console.ReadLine();

            //出力
            Console.WriteLine((a + b + c) + " " + s);
        }

        // 要素をシーケンスに追加するユーティリティ
        public static IEnumerable<T> Before<T>(this IEnumerable<T> items, T first)
        {
            yield return first;

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

        public static IEnumerable<IEnumerable<T>> Comb<T>(this 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 c.Before(x);

                    i++;
                }
            }
        }
    }
}