Hypothesis Tests · Superchallenge problem

A die is rolled twice to test $H_0$: the die is fair, against $H_1$: the die shows 6 with probability $\tfrac12$ and each other face with probability $\tfrac1{10}$. You may reject $H_0$ on any set of the 36 ordered outcomes, provided the probability of rejecting under $H_0$ is at most $0.05$. What is the largest possible power (probability of rejecting under $H_1$)? Give a fraction.