Problem D
Common Factors
Everyone likes to share things in common with other people.
Numbers are the same way! Numbers like it when they have a factor in common.
For example, $4$ and $6$ share a common factor of $2$, which gives them something to talk about.
For a given integer $n$, we define a function, $f(n)$, equal to the number of integers in the range $\left[1, n\right]$ that share a common factor greater than $1$ with $n$.
Furthermore, we can define a second function, $g(n)$, which characterizes the fraction of numbers that like a given number as follows: $g(n)$ = $\frac{f(n)}{n}$
What we really want to know though, is, for any integer $2 \leq k \leq n$, what is the maximum value of $g(k)$?
Input
The input consists of a single integer $n$ ($2 \leq n \leq 10^{18}$), the value of $n$ for the input case.
Output
For the provided test case, output the result as a fraction, in lowest terms, in the form $p$/$q$ where the greatest common divisor of $p$ and $q$ is $1$.
| Sample Input 1 | Sample Output 1 |
|---|---|
10 |
2/3 |
| Sample Input 2 | Sample Output 2 |
|---|---|
100 |
11/15 |
