200 kyr integration of the nine largest (H < 13.5) NEOs. The integration was carried out with the BS integrator without GR and Yarkovsky. The red unstable orbit corresponds to the exceptional case of (3552) Don Quixote, a near-Earth comet on a Jupiter-crossing orbit (a ~ 4.2 au, e ~ 0.71, and i ~ 31°), and the blue orbit evolving to small perihelion distance is (2212) Hephaistos, which is predicted to be destroyed in an encounter with the Sun in about 100 kyr.