Those are indeed the three subdivisions, but according to Wikipedia the Federation of Bosnia and Herzegovina and the Republika Srpska are called entities, and for ease of typing I have removed the "Federation of" and "Republika" from the answers. Brcko is indeed a distrikt, as is written in the blue header above it. I will check the type-ins to make sure the longer names are also accepted though.
Federation of bosnia and herzegovina,
Republic of srpska,
Brčko distrikt