After a big bang a new universe was created containing just three atoms: hydrogem, nitrogem and oxygem. At any time a single atom of any type splits into one each of the other two types and is itself destroyed in the process. For instance, one atom of hydrogem splits into one atom of nitrogem along with one atom of oxygem. Determine if it is possible that at some time there would be 2001 more hydrgem atoms than oxygem atoms.

[This problem comes from the University of Sydney Mathematics Enrichment Group 15 June 2001 problem sheet. Thank you to our friends in Sydney for permission for NRICH to use it.]