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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _init_from_dict(self, model_dict):
 """ Initiate self from a model_dict to make sure attributes such as vars, params are available. Creates lists of alphabetically sorted independent vars, dependent vars, sigma vars, and parameters. Finally it creates a signature for this model so it can be called nicely. This signature only contains independent vars and params, as one would expect. :param model_dict: dict of (dependent_var, expression) pairs. """

        sort_func = lambda symbol: symbol.name
        self.model_dict = OrderedDict(sorted(model_dict.items(),
                                             key=lambda i: sort_func(i[0])))
        # Everything at the bottom of the toposort is independent, at the top
        # dependent, and the rest interdependent.
        ordered = list(toposort(self.connectivity_mapping))
        independent = sorted(ordered.pop(0), key=sort_func)
        self.dependent_vars = sorted(ordered.pop(-1), key=sort_func)
        self.interdependent_vars = sorted(
            [item for items in ordered for item in items],
            key=sort_func
        )
        # `independent` contains both params and vars, needs to be separated
        self.independent_vars = [s for s in independent if
                                 not isinstance(s, Parameter) and not s in self]
        self.params = [s for s in independent if isinstance(s, Parameter)]

        try:
            assert not any(isinstance(var, Parameter)
                           for var in self.dependent_vars)
            assert not any(isinstance(var, Parameter)
                           for var in self.interdependent_vars)
        except AssertionError:
            raise ModelError('`Parameter`\'s can not feature in the role '
                             'of `Variable`')
        # Make Variable object corresponding to each depedent var.
        self.sigmas = {var: Variable(name='sigma_{}'.format(var.name))
                       for var in self.dependent_vars}