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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.Collectors;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        String V = scan.nextLine();
        String C = scan.nextLine();
        final List<Integer> v = Arrays.stream(V.split(" ", N)).mapToInt(Integer::parseInt).boxed().collect(Collectors.toList());
        final List<Integer> c = Arrays.stream(C.split(" ", N)).mapToInt(Integer::parseInt).boxed().collect(Collectors.toList());
        System.out.println(find(N, 0, new HashSet<>(), v, c));
    }

    public static int find(int N, int cMax, Set<Integer> mark, List<Integer> v, List<Integer> c) {
        int max = 0;
        for (int i = 0; i < N; i++) {
            if (!mark.contains(i)) {
                final int i1 = cMax + v.get(i) - c.get(i);
                if (i1 > max) {
                    max = i1;
                }
                mark.add(i);
                int sMax = find(N, max, mark, v, c);
                if (sMax > max) {
                    max = sMax;
                }
                mark.remove(i);
            }
        }
        return max;
    }

}