@overlay doesn't play nicely with None

[pyhedgehog]

@overload
def f1(o: NoneType) -> str:
    return 'None'
@overload
def f1(o: int) -> str:
    return type(o).__name__
@overload
def f1(o: str) -> str:
    return type(o).__name__
print(f1(''))
print(f1(0))
print(f1(None))

Will fail with optional is None. I've found workaround:

@overload
def f1(o: Optional[NoneType]=None) -> str:
    return 'None'
@overload
def f1(o: Optional[int]) -> str:
    if o is None: return f1()
    return type(o).__name__
@overload
def f1(o: Optional[str]) -> str:
    if o is None: return f1()
    return type(o).__name__
print(f1(''))
print(f1(0))
print(f1(None))
print(f1())

This works, but this is awful. Especially awful is need to add if o is None to every variant (calls lexically last variant).
Any hints?