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: Accepted)

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

class Program
{
    int n;
    int[] v, c;
    void Run()
    {
        var sc = new Scanner();
        n = sc.NextInt();
        v = new int[n];
        for (int i = 0; i < n; i++) v[i] = sc.NextInt();
        c = new int[n];
        for (int i = 0; i < n; i++) c[i] = sc.NextInt();

        Console.WriteLine(Dfs(0, 0, 0));
    }

    int Dfs(int index, int x, int y)
    {
        if (index == n) return x - y;
        int max = 0;
        int res;
        res = Dfs(index + 1, x + v[index], y + c[index]);
        if (res > max) max = res;
        res = Dfs(index + 1, x, y);
        if (res > max) max = res;
        return max;
    }

    static void Main(string[] args)
    {
        new Program().Run();
    }
}

class UnionFindTree
{
    private int[] p;
    private int[] d;

    public UnionFindTree(int size)
    {
        p = new int[size];
        d = new int[size];
        for (int i = 0; i < size; i++) p[i] = i;
    }

    public int Find(int x)
    {
        if (p[x] == x) return x;
        return p[x] = Find(p[x]);
    }

    public void Unite(int x, int y)
    {
        int px = Find(x);
        int py = Find(y);
        if (px == py) return;

        if (d[px] < d[py])
        {
            p[px] = py;
        }
        else
        {
            p[py] = px;
            if (d[px] == d[py]) d[px]++;
        }
    }

    public bool Same(int x, int y)
    {
        return Find(x) == Find(y);
    }
}

class Scanner
{
    int index = -1;
    string[] buf;

    public Scanner()
    {
    }

    public int NextInt()
    {
        CheckNext();
        return int.Parse(buf[index++]);
    }

    public long NextLong()
    {
        CheckNext();
        return long.Parse(buf[index++]);
    }

    public double NextDouble()
    {
        CheckNext();
        return double.Parse(buf[index++]);
    }

    public string NextString()
    {
        CheckNext();
        return buf[index++];
    }

    private void CheckNext()
    {
        if (index >= 0 && index < buf.Length) return;

        buf = Console.ReadLine().Split(' ');
        index = 0;
    }
}