Dynamic function mapping

I'm currently playing around with Design Patterns in Python. I tried to write a generic Proxy which counts calls to attributes/functions. This works fine with getattr for own types, but doesn't work for stuff like str(), len() etc. So I tried dynamically remapping the function calls to the functions of the child object, but It doesn't work. Anyone can help me out on this?

class CountAccessProxy():
  def __init__(self, obj):
    self._obj = obj
    self.updateFuncs(dir(obj))
    self.countAccess={}
    print(self.__dict__)

  def __getattr__(self, att):
    self.countAccess[att]= self.countAccess.setdefault(att, 0) +1
    return getattr(self._obj, att)

  def updateFuncs(self,funcs):
    for func in funcs:
      if "__" in func:
        #Try to remap the functions to the functions of child obj
        self.__dict__[func] = getattr(self._obj,func)


listy = CountAccessProxy([0,2,5,5])
print(len(listy))

Traceback (most recent call last):
  File "proxy.py", line 52, in <module>
    print(len(listy))
TypeError: object of type 'CountAccessProxy' has no len()