During a day, 2016 customers visited the store. Each customer visited the store only once (a customer enters the store, spends some time, and then leaves). Find the greatest integer $k$ such that the following statement is always true:

We can find $k$ customers such that either all of them have been at the store at the same time, or any two of them have not been at the store at the same time.

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