24403번 - Common Factors 다국어

문제

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ドル$ and 6ドル$ share a common factor of 2ドル,ドル which gives them something to talk about.

For a given integer $n,ドル we define a function, $f(n),ドル equal to the number of integers in the range [1ドル,ドル $n$] that share a common factor greater than 1ドル$ with $n$.

Furthermore, we can define a second function, $g(n),ドル 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ドル ≤ k ≤ n,ドル what is the maximum value of $g(k)$?

입력

The input consists of a single integer $n$ (2ドル ≤ n ≤ 10^{18}$), the value of $n$ for the input case.

출력

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.

제한

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