Who was older, LUO Guan-zhong or SHI Nai-an? And Which One Appeared Earlier, Romance of the Three Kingdoms or The Outlaws of Marsh?

When talking about the relation between LUO Guanzhong and SHI Nai-an, most people think that the former was younger than the latter and was the pupil of the latter. And when talking about Romance of the Three Kingdoms and The Outlaws of Marsh, they believe that the former appeared later. However, the relevant historical documents prove that it was not true. And the fact is that LUO was older than SHI and Romance of the Three Kingdoms appeared earlier than The Outlaws of Marsh.