The preparation of homeopathic "remedies" involves the repeated dilution of solutions containing an active ingredient such as arsenic trioxide (As2O3). Suppose one begins with 64.0 g of arsenic trioxide dissolved in water, and repeatedly dilutes the solution with pure water, each dilution reducing the amount of arsenic trioxide in the solution by a factor of 100. Assuming perfect mixing at each dilution, what is the maximum number of dilutions one may perform such that at least one molecule of arsenic trioxide remains in the diluted solution?