Fix Python – Nested defaultdict of defaultdict

Is there a way to make a defaultdict also be the default for the defaultdict? (i.e. infinite-level recursive defaultdict?)
I want to be able to do:
x = defaultdict(…stuff…)
x[0][1][0]
{}

So, I can do x = defaultdict(defaultdict), but that’s only a second level:
x[0]
{}
x[0][0]
KeyError: 0

There are recipes that can do this. But can it be don….