On day 0, you take a long-distance flight and you are infected with COVID with probability 1/2. Being a responsible citizen, you decide to quarantine for 14 days. You also visit a wizard, who gives you some special beans to help cure you, just in case you are sick. You take the beans every day, starting on day 1 of your quarantine. Each day, the beans have a 1/8 chance of immediately curing you. Suppose you are tested at the end of day 14 (after 14 days of taking beans) and the test comes back negative. What is the probability that you were actually infected with COVID on day 0? Assume that the test is fully accurate.