You have very loyal rats that are willing to taste cups of wine for you! Exactly one of the cups has poison in it, which kills rats that drink it one hour after sipping. Otherwise, the rat drinks wine and feels a little tipsy, but it powers through and is fine. The rats are busy, so they can only drink cups within a one-hour period. Find the maximum value of such that the poisonous cup can be uniquely identified when . Assume the sipping process is instantaneous.