#bic

Two logistic regression models have 2 and 3 parameters. On the first $n$ training examples, their maximized log-likelihoods satisfy $L_2(n) - L_1(n) = 0.01\,n$. With $\mathrm{BIC} = L - \frac{d}{2}\ln n$, BIC prefers model 1 for small $n \ge 2$. What is the smallest $n \ge 2$ at which BIC prefers model 2?