Systems and methods are provided for authenticating an input device subsystem for operation with a host. Different instruments are used to play the musical notes. The rotation is transmitted to the re-orientable elements by transmission elements having sufficient play so that the indexing accuracy is not impaired. Since the generation of heat caused by fuel of the main injection occurs after the generation of heat caused by fuel of the early-stage injection has been completed, there is no sudden entry of fuel injected by the main injection into the hot flame inside the cylinder; accordingly, the aggravation of smoke is prevented.