Problem Statement

You are given multisets with N non-negative integers each: A=${ a_1,\ldots,a_N$} and B=${ b_1,\ldots,b_N$ }.
You can perform the operations below any number of times in any order.

• Choose a non-negative integer x in A. Delete one instance of x from A and add one instance of 2x instead.
• Choose a non-negative integer x in A. Delete one instance of x from A and add one instance of $\left\lfloor \frac{x}{2} \right\rfloor instead. (\lfloor x \rfloor$ is the greatest integer not exceeding x.)

Your objective is to make A and B equal (as multisets).
Determine whether it is achievable, and find the minimum number of operations needed to achieve it if it is achievable.

Input

Input is given from Standard Input in the following format:
N
$a_1 \ldots a_N$
$b_1 \ldots b_N$

Output

If the objective is achievable, print the minimum number of operations needed to achieve it; otherwise, print -1.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq a_1 \leq \ldots \leq a_N \leq 10^9$
• $0 \leq b_1 \leq \ldots \leq b_N \leq 10^9$
• All values in input are integers.

Sample Input 1

3
3 4 5
2 4 6

Sample Output 1

2

You can achieve the objective in two operations as follows.

• Choose x=3 to delete one instance of x\, (=3) from A and add one instance of 2x\, (=6) instead. Now we have A={4,5,6}.
• Choose x=5 to delete one instance of x\, (=5) from A and add one instance of $\left\lfloor \frac{x}{2} \right\rfloor$ \, (=2) instead. Now we have A={2,4,6}.

Sample Input 2

1
0
1

Sample Output 2

-1

You cannot turn { 0 } into { 1 } .

见题面 Input 部分

见题面 Output 部分