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 Ruby (2.3.3) (judge verdict: Runtime Error)

require "prime"

N = gets.to_i
a = gets.chomp.split(' ').map(&:to_i)
b = gets.chomp.split(' ').map(&:to_i)
flags = a.map.with_index {|item, i| item > b[i]*2 || item == b[i]}
if flags.all?
  if a == b
    cost = 0
  elsif b.all? {|item| item == 0}
    cost = 2
  else
    b.each_with_index do |item, i|
      if item == 0
        a.delete_at(i)
        b.delete_at(i)
      end
    end
    powers = []
    a.each_with_index do |item, i|
      primes = []
      Prime.prime_division(item - b[i]).each do |array|
        primes << array[0]
      end
      power = primes.select {|prime| b[i] < prime && b[i] % prime != 0}.min
      powers << power
    end
    cost = powers.inject(0) {|sum, k| sum + 2 ** k}
  end
else
  cost = -1
end
puts cost