A list of positive integers is called *good* if the maximum element of the list appears exactly once. A *sublist* is a list formed by one or more consecutive elements of a list. For example, in the list $10, 34, 34, 22, 30, 22$, the sublist $22, 30, 22$ is good, while $10, 34, 34, 22$ is not.

A list is *very good* if all its sublists are good. Find the minimum value of $k$ such that there exists a very good list of length $2019$ with $k$ different values in it.

Let's think step by step and output the final answer within \boxed{}.
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