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.

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.

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.