A survey researcher wants to estimate the prevalence of a rare disease (prevalence $p = 0.01$). If they want to use a cluster sample with a total sample size $n = 400$, and the intra-class correlation is $\rho = 0.05$, what is the effective sample size $n_{eff}$? Note: $n_{eff} = \frac{n}{1 + (m-1)\rho}$, assume cluster size $m = 20$.