assert data["context_b"] == "started b"
    assert data["context_a"] == "started a"
    assert data["bg"] == "not set"
    middleware_state = json.loads(response.headers["x-state"])
    assert middleware_state["context_b"] == "started b"
    assert middleware_state["context_a"] == "started a"
    assert middleware_state["bg"] == "not set"
    assert state["context_b"] == "finished b with a: started a"
    assert state["context_a"] == "finished a"

        )

        self.user_middleware: list[Middleware] = (
            [] if middleware is None else list(middleware)
        )
        self.middleware_stack: Union[ASGIApp, None] = None
        self.setup()

    def build_middleware_stack(self) -> ASGIApp:
        # Duplicate/override from Starlette to add AsyncExitStackMiddleware