Asynchronous Challenge

Bill Gates is visiting Annenberg Hall every day for only a second, but he never advertises the time he shows up. You are only at Visitas for two days, and you really want to see Bill Gates in the flesh, so you’ll visit Annenberg Hall for the two days (unless you commit to Harvard, then you can see Bill Gates every day). You know for sure that he visits between 12 am and 6 am, and the Bill Gates Harvard Tracker has his visiting time data for the last month (30 days). You want to arrive before Bill Gates, and you will wait indefinitely until he shows up. However, you want to have a good place in line and will be a little bit sadder if you show up behind other people (i.e., submissions). In short, you want to maximize the following function: (time you arrive) - 5 × (number of people who showed up before you), if you showed up before Bill Gates, but the minimum score if you show up after Bill. Submit the times that you want to show up for each day!