Krull dimension localization with coefficients

Question

Let $A[x_1, \ldots, x_n]$ be a polynomial ring over an integral domain, $A$. Let $s = a\prod_{1\leq i \leq n}{x_i}^{\alpha_i}$, $a \in A$. What is the Krull dimension of $A[x_1, \ldots, x_n]_s$?