Candy Density

Seongwon is a guest at an algorithm camp and makes candy for the participants. There are $N$ participants, numbered 0 to $N-1$.

Participant $i$ holds a basket with a capacity of $C_i$ liters and wants to receive $W_i$ grams of candy.

Seongwon fills every basket to its capacity, so participant $i$ receives exactly $C_i$ liters of candy. He can make only one kind of candy, so a single density $d$ (grams per liter) applies to all of it. He may choose any positive real number for $d$.

Once the density is $d$, participant $i$ actually receives $d \times C_i$ grams. To satisfy as many participants as possible, Seongwon picks the $d$ that minimizes the total difference between the requested weight and the received weight:

$\sum_{i=0}^{N-1} \left| W_i - d \times C_i \right|$

Write a program that computes this minimum.

The first line contains the number of participants $N$ ($1 \le N \le 50$).

The second line contains $C_0, C_1, \dots, C_{N-1}$ and the third line contains $W_0, W_1, \dots, W_{N-1}$, separated by spaces. ($1 \le C_i, W_i \le 1000000$)

Print the minimum total difference on one line as a reduced fraction.

The minimum is always a rational number. Write it as $p / q$, where $p$ is a nonnegative integer, $q$ is a positive integer, and $\gcd(p, q) = 1$. If $q = 1$, print only p; otherwise print it in the form p/q. A decimal or an approximate value is not accepted.