What type of government did the Sumerians have?

So i'm doing a report on this and i'm doing the classical period of Sumer (with the epic of gilgamesh, ziggurats, city-states, polytheistic etct) and i know they had city-states and a high priest that was for each state but was there a single king who ruled over all of them? Or was their just individual kings that ruled over each city state? or were they're both individual kings and then a higher king?!? PLEASE HELP THIS IS IMPORTANT (: oh and remember this is the CLASSICAL period, not the one after or anything! thank youu in advance!