Problem Statement

You are given length-$N$ integer sequences $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$. Consider length-$N$ sequences of rational numbers $c=(c_1,c_2,\dots,c_N)$ and $d=(d_1,d_2,\dots,d_N)$ that satisfy the following condition.

• $(A_i+c_i)(B_j+d_j)=(A_j+c_j)(B_i+d_i)$ for all $1 \le i,j \le N$.

Find the minimum possible value of $\displaystyle \sum_{i=1}^{N} \left ( |c_i|+|d_i| \right )$.

It can be proved that the answer to this problem can be uniquely represented as an irreducible fraction $p/q$ with a positive denominator and a non-negative numerator. Output these $p$ and $q$.

Constraints

• All input values are integers.
• $2 \le N \le 2 \times 10^5$
• $|A_i|, |B_i| \le 10^6$

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N
B_1 B_2 \dots B_N

Output

When the answer to this problem is represented as an irreducible fraction $p/q$ with a positive denominator and a non-negative numerator, output it in the following format:

p q