Problem:
Score : 700 points

Problem Statement

Aoki is playing with a sequence of numbers a_{1}, a_{2}, ..., a_{N}. Every second, he performs the following operation :

Choose a positive integer k. For each element of the sequence v, Aoki may choose to replace v with its remainder when divided by k, or do nothing with v. The cost of this operation is 2^{k} (regardless of how many elements he changes).

Aoki wants to turn the sequence into b_{1}, b_{2}, ..., b_{N} (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.

Constraints

1 \leq N \leq 50

0 \leq a_{i}, b_{i} \leq 50

All values in the input are integers.

Input

Input is given from Standard Input in the following format:

N
a_{1} a_{2} ... a_{N}
b_{1} b_{2} ... b_{N}

Output

Print the minimum cost required to turn the original sequence into b_{1}, b_{2}, ..., b_{N}. If the task is impossible, output -1 instead.

Sample Input 1

3
19 10 14
0 3 4

Sample Output 1

160

Here's a possible sequence of operations :

Choose k = 7. Replace 19 with 5, 10 with 3 and do nothing to 14. The sequence is now 5, 3, 14.

Choose k = 5. Replace 5 with 0, do nothing to 3 and replace 14 with 4. The sequence is now 0, 3, 4.

The total cost is 2^{7} + 2^{5} = 160.

Sample Input 2

3
19 15 14
0 0 0

Sample Output 2

2

Aoki can just choose k = 1 and turn everything into 0. The cost is 2^{1} = 2.

Sample Input 3

2
8 13
5 13

Sample Output 3

-1

The task is impossible because we can never turn 8 into 5 using the given operation.

Sample Input 4

4
2 0 1 8
2 0 1 8

Sample Output 4

0

Aoki doesn't need to do anything here. The cost is 0.

Sample Input 5

1
50
13

Sample Output 5

137438953472

Beware of overflow issues.

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

def rem(x,r):
  if x <= 2*r:
    return -1
  ret = []
  for i in range(1,x):
    if x%i == r:
      ret.append([i])
    else:
      s = rem(x%i,r)
      if s == -1:
        continue
      else:
        for j in s:
          if j == -1:
            continue
          elif j[-1] < i:
            ret.append([i]+j)
          else:
            ret.append([i]+j)
  return ret
n = int(input())
x = list(map(int,input().split()))
y = list(map(int,input().split()))
for xx,yy in zip(x,y):
  if xx != yy and rem(xx,yy) == -1:
    print(-1)
    exit()
ls = [rem(xx,yy) if xx != yy else 0 for xx,yy in zip(x,y)]
mxls = [ls[i][0][0] if type(ls[i]) == list else 0 for i in range(n)]
mx = max(mxls)
ansst = set()
ansst.add(mx)
flg = [0]*n
while True:
  for i in range(n):
    if mxls[i] == mx or x[i]%mx == y[i]:
      flg[i] = 1
      mxls[i] = 0
      continue
    r = rem(x[i]%mx,y[i])
    if r != -1 and r[0][0] <= mxls[i]:
      mxls[i] = r[0][0]
      x[i] %= mx
  mx = max(mxls)
  ansst.add(mx)
  if flg.count(1) == n:
    break
ans = -1
for b in ansst:
  ans += 2**b
print(ans)