  We prove a structure theorem for the connected coassociative magmatic
bialgebras. The space of primitive elements is an algebra over an operad called
the primitive operad. We prove that the primitive operad is magmatic generated
by n-2 operations of arity n. The dimension of the space of all the n-ary
operations of this primitive operad turns out to be the Fine number F_{n-1}. In
short, the triple of operads (As, Mag, MagFine) is good.
