$depth$ of the integral closure of a notherian local domain.

Question

Let $(R,\mathfrak m)$ be a 3 dimensional notherian domain of finite-type over field $k$ and let $\overline R$ denotes its integral closure in fraction field. $\overline R$ is finite $R$-module and if $\mathfrak n$ is a maximal ideal of $\overline R$, we know $depth_{\overline R_n} \overline R_n \geq 2$. Also clearly, $depth_{ R} \overline R \geq 1$ . So, can we also say that $depth_{ R} \overline R \geq 2$. any hints/ideas?