Tor algebra of local rings with decomposable maximal ideal

Let $(R,{\mathfrak{m}}_R)$ be a commutative noetherian local ring. Assuming that ${\mathfrak{m}}_R=$$I\oplus J$ is a direct sum decomposition, where $I$ and $J$ are non-zero ideals of $R$, we describe the structure of the Tor algebra of $R$ in terms of the Tor algebras of the rings $R\mathrm{/}I$ and $R\mathrm{/}J$.