In Irish, instead of saying "Hello!" or "Good morning!" what you say is a bit more complicated.
If person one says: Dia dhuit!
Person two answers: Dia's Muire dhuit!
However, if the first person is showing off or is feeling particularly ebullient, he or she could start with: Dia's Muire agus Padraig dhuit!
To which the proper reply would be: Dia's Muire agus Padraig agus Brigid dhuit!
Under no circumstance can you simply repeat what was said to you (thus the one-upmanship). What I find wonderful is that none of these actually mean "Hi!" or "Good morning!" To translate them literally, Dia dhuit is "God be with you;" Dia's Muire dhuit is "God and Mary be with you;" Dia's Muire agus Padraig dhuit is "God, Mary, and Patrick be with you;" lastly would be "God, Mary, Patrick, and Brigid be with you." Thus the reason for the one-upmanship is simply wishing the other more well (or at least more aid from Ireland's favored saints).