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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 __definitions_descriptor(self):
 """Describes the definitions section of the OpenAPI spec. Returns: Dictionary describing the definitions of the spec. """

    # Filter out any keys that aren't 'properties' or 'type'
    result = {}
    for def_key, def_value in self.__parser.schemas().iteritems():
      if 'properties' in def_value or 'type' in def_value:
        key_result = {}
        required_keys = set()
        if 'type' in def_value:
          key_result['type'] = def_value['type']
        if 'properties' in def_value:
          for prop_key, prop_value in def_value['properties'].items():
            if isinstance(prop_value, dict) and 'required' in prop_value:
              required_keys.add(prop_key)
              del prop_value['required']
          key_result['properties'] = def_value['properties']
        # Add in the required fields, if any
        if required_keys:
          key_result['required'] = sorted(required_keys)
        result[def_key] = key_result

    # Add 'type': 'object' to all object properties
    # Also, recursively add relative path to all $ref values
    for def_value in result.itervalues():
      for prop_value in def_value.itervalues():
        if isinstance(prop_value, dict):
          if '$ref' in prop_value:
            prop_value['type'] = 'object'
          self._add_def_paths(prop_value)

    return result