# Specifying priors in rstanarm for hierarchical model

We are given the model \begin{align*} y_{ij} & \sim \mathsf{Normal}(\alpha_j + \beta x_i, \sigma^2)\\ \alpha_j & \sim \mathsf{Normal}(\gamma_0 + \gamma_1 u_j, \tau^2) \end{align*} with priors \begin{align*} \beta, \gamma_0, \gamma_1 & \sim \mathsf{Normal}(0, 0.5^2)\\ \sigma, \tau & \sim \mathsf{Normal}_+(0, 0.25^2) \end{align*} where we have $$j$$ counties and $$i$$ observations. I'm having trouble specifying all of my priors for rstanarm. What I have so far is

library(rstan)
library(rstanarm)