There are $2016$ customers who entered a shop on a particular day. Every 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 back).
Find the maximal $k$ such that the following 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.