There are $2016$ customers who entered a shop on a particular day. Each customer entered the shop exactly once (i.e., the customer entered the shop, stayed there for some time, and then left the shop without returning).

Find the maximal $k$ such that the following condition holds:

There are $k$ customers such that either all of them were in the shop at a specific time instance, or no two of them were both in the shop at any time instance.

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