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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 auth_publickey(self, username, key, event=None):
 """ Authenticate to the server using a private key. The key is used to sign data from the server, so it must include the private part. If an ``event`` is passed in, this method will return immediately, and the event will be triggered once authentication succeeds or fails. On success, `is_authenticated` will return ``True``. On failure, you may use `get_exception` to get more detailed error information. Since 1.1, if no event is passed, this method will block until the authentication succeeds or fails. On failure, an exception is raised. Otherwise, the method simply returns. If the server requires multi-step authentication (which is very rare), this method will return a list of auth types permissible for the next step. Otherwise, in the normal case, an empty list is returned. :param str username: the username to authenticate as :param .PKey key: the private key to authenticate with :param .threading.Event event: an event to trigger when the authentication attempt is complete (whether it was successful or not) :return: list of auth types permissible for the next stage of authentication (normally empty) :raises: `.BadAuthenticationType` -- if public-key authentication isn't allowed by the server for this user (and no event was passed in) :raises: `.AuthenticationException` -- if the authentication failed (and no event was passed in) :raises: `.SSHException` -- if there was a network error """

        if (not self.active) or (not self.initial_kex_done):
            # we should never try to authenticate unless we're on a secure link
            raise SSHException("No existing session")
        if event is None:
            my_event = threading.Event()
        else:
            my_event = event
        self.auth_handler = AuthHandler(self)
        self.auth_handler.auth_publickey(username, key, my_event)
        if event is not None:
            # caller wants to wait for event themselves
            return []
        return self.auth_handler.wait_for_response(my_event)