P10618 [ICPC 2013 WF] Factors

The fundamental theorem of arithmetic states that every integer greater than $1$ can be uniquely represented as a product of one or more primes. While unique, several arrangements of the prime factors may be possible. For example: - $10=2\times 5=5\times 2$； - $20=2\times 2\times 5=2\times 5\times 2=5\times 2\times 2$； Let $f(k)$ be the number of different arrangements of the prime factors of $k$. So $f(10) = 2$ and $f(20) = 3$. Given a positive number $n$, there always exists at least one number $k$ such that $f(k) = n$. We want to know the smallest such $k$.

The input consists of at most $1 000$ test cases, each on a separate line. Each test case is a positive integer $n < 2^{63}$.

For each test case, display its number $n$ and the smallest number $k > 1$ such that $f(k) = n$. The numbers in the input are chosen such that $k < 2^{63}$.