In a city, there are $2019$ metro stations. Some pairs of stations are connected by tunnels, and from any station, you can reach any other station through these tunnels. The mayor ordered the organization of several metro lines: each line should include several different stations connected in series by tunnels (several lines can pass through the same tunnel), and each station must be on at least one line. To save money, no more than $k$ lines should be made. It turned out that the mayor's order is not feasible. What is the largest value of $k$ for which this could happen?

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