Hypothesis Tests · Superchallenge problem

A single observation $X$ is taken. Under $H_0$ it has density $f_0(x) = 1$ on $(0,1)$; under $H_1$ it has density $f_1(x) = 2x$ on $(0,1)$. Among all tests with significance level $0.05$, the Neyman–Pearson lemma says the most powerful one rejects when the likelihood ratio $f_1(X)/f_0(X)$ is large. What is the power of this most powerful test? Give a fraction.