I'm arriving into Changi (United flight) around 1230AM and leaving on an Indigo flight around 545AM. I'd like to work out (go for a run) and shower if possible. What are my options? I see the transit hotel has a gym in T1/T2 according to this page

http://www.harilelahospitality.com/services_gym.html

but I am not sure what terminal I'll arrive in (and if I can move around easily).