My parents are getting their roof redone this fall. It's a variation of a mansard roof - basically flattish roof (pitched towards a drain in the middle), and second floor walls hidden by not-quite-vertical shingled roof sections.

I suggested this would be a good time to rectify a bathroom fan venting issue (builder didn't install them back in '70s since there's a window in bathroom, and at some point a fan was installed but just vents in the foot-high ventilated attic/roof cavity - yuck). Roofer is more than willing to cut in and seal whatever vent cap the client wants but the question is:

Would you go up through the flat(ish) roof (high enough to clear typical snowload)? Or vent it sideways (away from windows I suppose) through sloped shingle section, which might mean a longer duct?

Fan is a 110 cfm pretty standard unit, 4" duct if it makes any difference.

Thanks for any advice you can offer. Archived posts and Hvac-Calc already saved them from installing an oversized central air unit two years ago (3 quotes but contractors were all sizing it on square footage alone, half to one ton bigger than what the calc came up with).