Do zombies poop?

[Aoi Magi]

First a little backstory, I am supposed to finish up a report as soon as possible now, after I stayed up the entire night to finish the project, and the report is supposed to be my boss's job, not mine. So between my daily plans to murder him and turn him into my undead slave, and vorlon's thread, I had this sudden thought, do zombie's poop? After all, they keep trying to eat people constantly, so where do they store all that meat? Every zombie infested city is generally shiny and spotless, so they definitely don't poop outside, but I don't expect them to have the decency to visit the loo after each undigested meal. But even if they did, who the f*** cleans up after them? Cause after a few weeks, I'd expect the survivors to either wear vader-helmets or die due to sheer stench... ah this is so confusing.