A flexible, uniform chain of total mass \(M\) and length \(L\) rests on a frictionless horizontal tabletop. Initially, a length \(y_0\) of the chain hangs vertically over the edge of the table, and the chain is released from rest. As the chain slides off the table, the portion on the table moves horizontally toward the edge while the hanging portion falls vertically.

What is the total work done by the gravitational force on the chain from the moment of release until the instant the entire chain leaves the horizontal tabletop?