),
    ] = "https://fastapi.tiangolo.com/img/favicon.png",
    oauth2_redirect_url: Annotated[
        Optional[str],
        Doc(
            """
            The OAuth2 redirect URL, it is normally automatically handled by FastAPI.
            """
        ),
    ] = None,
    init_oauth: Annotated[
        Optional[Dict[str, Any]],
        Doc(
            """

    sub_router_shutdown: bool = False


@pytest.fixture
def state() -> State:
    return State()


@pytest.mark.filterwarnings(
    r"ignore:\s*on_event is deprecated, use lifespan event handlers instead.*:DeprecationWarning"
)
def test_router_events(state: State) -> None:
    app = FastAPI()

    @app.get("/")
    def main() -> Dict[str, str]:
        return {"message": "Hello World"}

        or hasattr(origin, "__pydantic_core_schema__")
        or hasattr(origin, "__get_pydantic_core_schema__")
    )


def field_annotation_is_scalar(annotation: Any) -> bool:
    # handle Ellipsis here to make tuple[int, ...] work nicely
    return annotation is Ellipsis or not field_annotation_is_complex(annotation)


def field_annotation_is_scalar_sequence(annotation: Union[Type[Any], None]) -> bool: