You have 2016 sticks of the same length in a box. You pick a stick at random, break it into two **equal halves**, and put them back in for a total of 2017 sticks. You repeat this process of *random picking and breaking* indefinitely.

What is the maximum value of \(x\) such that, at *any time during this process*, you are guaranteed to have at least \(x\) sticks of the same length?

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