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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		int[] v = new int[n];
		int[] c = new int[n];
		for (int i = 0; i < v.length; i++) {
			v[i] = Integer.parseInt(sc.next());
		}
		for (int i = 0; i < c.length; i++) {
			c[i] = Integer.parseInt(sc.next());
		}
		int ans = 0;
		for (int i = 0; i < (1 << n - 1); i++) {
			int sum = 0;
			int tmp = v[0] - c[0];
			for (int j = 0; j < n - 1; j++) {
				if ((i & (1 << j)) != 0) {
					sum += tmp;
					tmp = v[j + 1] - c[j + 1];
				} else {
					tmp = v[j + 1] - c[j + 1];
				}
			}
			ans = Math.max(ans, sum + tmp);
		}
		System.out.println(ans);

		sc.close();
	}
}