Judging by lore, abilities and characterization, what would Dottore's IQ realistically be?

I know he's fictional and we can't make him take a test, but there's already people doing qualifies guesses on the IQs of dead people like Nikola Tesla, Thomas Edison, ect. so Dottore's IQ can probably be figured out somehow.

(Obligatory didn't post this in Dottormains because reasons)