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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 model_schema( model: Type['main.BaseModel'], by_alias: bool = True, ref_prefix: Optional[str] = None ) -> Dict[str, Any]: """ Generate a JSON Schema for one model. With all the sub-models defined in the ``definitions`` top-level JSON key. :param model: a Pydantic model (a class that inherits from BaseModel) :param by_alias: generate the schemas using the aliases defined, if any :param ref_prefix: the JSON Pointer prefix for schema references with ``$ref``, if None, will be set to the default of ``#/definitions/``. Update it if you want the schemas to reference the definitions somewhere else, e.g. for OpenAPI use ``#/components/schemas/``. The resulting generated schemas will still be at the top-level key ``definitions``, so you can extract them from there. But all the references will have the set prefix. :return: dict with the JSON Schema for the passed ``model`` """

    ref_prefix = ref_prefix or default_prefix
    flat_models = get_flat_models_from_model(model)
    model_name_map = get_model_name_map(flat_models)
    m_schema, m_definitions = model_process_schema(
        model, by_alias=by_alias, model_name_map=model_name_map, ref_prefix=ref_prefix
    )
    if m_definitions:
        m_schema.update({'definitions': m_definitions})
    return m_schema