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.

3
19 10 14
0 3 4

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 $2^{7} + 2^{5} = 160$.

3
19 15 14
0 0 0

2

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

2
8 13
5 13

-1

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

4
2 0 1 8
2 0 1 8

0

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

1
50
13

137438953472

Beware of overflow issues.