BALTIC-WAY 1992 Problem 12

Let $\mathbb{N}$ denote the set of positive integers. Let $\varphi: \mathbb{N} \rightarrow \mathbb{N}$ be a bijective function and assume that there exists a finite limit

$$\lim _{n \rightarrow \infty} \frac{\varphi(n)}{n}=L$$

What are the possible values of $L$ ?