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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

n = int(input())
size = list(map(int, input().split()))
price = list(map(int, input().split()))

max_size = -1
max_price = -1
combination = []
ans = 0

for i in range(2**n-1) :
    tmp_sumS = 0
    tmp_sumP = 0
    tmp_comb = []
    over_flag = False

    for j in range(n) :
        # シフトして１ビットずつ判断
        is_put = i>>(n-j-1)&1
        tmp_comb.append(is_put)
        tmp_sumS += is_put * size[j]
        tmp_sumP += is_put * price[j]
            
        if tmp_sumS-tmp_sumP > ans:
            ans = tmp_sumS-tmp_sumP
    
    # over flag が立ってない かつ 暫定 max price より高いときに更新
    if (not over_flag) and tmp_sumP > max_price :
        max_price = tmp_sumP
        max_size = tmp_sumS
        combination = tmp_comb
    
print(ans)