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Solve the following problem using Python, implementing the functions described below, one line at a time
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<USER_TASK:>
Description:
 def patch_relationship(self, session, json_data, api_type, obj_id, rel_key):
 """ Replacement of relationship values. :param session: SQLAlchemy session :param json_data: Request JSON Data :param api_type: Type of the resource :param obj_id: ID of the resource :param rel_key: Key of the relationship to fetch """

        model = self._fetch_model(api_type)
        resource = self._fetch_resource(session, api_type, obj_id,
                                        Permissions.EDIT)
        if rel_key not in resource.__jsonapi_map_to_py__.keys():
            raise RelationshipNotFoundError(resource, resource, rel_key)
        py_key = resource.__jsonapi_map_to_py__[rel_key]
        relationship = self._get_relationship(resource, py_key,
                                              Permissions.EDIT)
        self._check_json_data(json_data)

        session.add(resource)
        remote_side = relationship.back_populates
        try:
            if relationship.direction == MANYTOONE:
                if not isinstance(json_data['data'], dict)\
                        and json_data['data'] is not None:
                    raise ValidationError('Provided data must be a hash.')

                related = getattr(resource, relationship.key)
                check_permission(related, None, Permissions.EDIT)
                check_permission(related, remote_side, Permissions.EDIT)

                setter = get_rel_desc(resource, relationship.key,
                                      RelationshipActions.SET)

                if json_data['data'] is None:
                    setter(resource, None)
                else:
                    to_relate = self._fetch_resource(
                        session, json_data['data']['type'],
                        json_data['data']['id'], Permissions.EDIT)
                    check_permission(to_relate, remote_side, Permissions.EDIT)
                    setter(resource, to_relate)
            else:
                if not isinstance(json_data['data'], list):
                    raise ValidationError('Provided data must be an array.')

                related = getattr(resource, relationship.key)

                remover = get_rel_desc(resource, relationship.key,
                                       RelationshipActions.DELETE)
                appender = get_rel_desc(resource, relationship.key,
                                        RelationshipActions.APPEND)
                for item in related:
                    check_permission(item, None, Permissions.EDIT)
                    remote = item.__mapper__.relationships[remote_side]
                    if remote.direction == MANYTOONE:
                        check_permission(item, remote_side, Permissions.EDIT)
                    else:
                        check_permission(item, remote_side, Permissions.DELETE)
                    remover(resource, item)

                for item in json_data['data']:
                    to_relate = self._fetch_resource(
                        session, item['type'], item['id'], Permissions.EDIT)
                    remote = to_relate.__mapper__.relationships[remote_side]

                    if remote.direction == MANYTOONE:
                        check_permission(to_relate, remote_side,
                                         Permissions.EDIT)
                    else:
                        check_permission(to_relate, remote_side,
                                         Permissions.CREATE)
                    appender(resource, to_relate)
            session.commit()
        except KeyError:
            raise ValidationError('Incompatible Type')

        return self.get_relationship(session, {}, model.__jsonapi_type__,
                                     resource.id, rel_key)