Best way to find product of $AD_i$ where $A$ is hermitian and $D_i$ is diagonal

Question

I have a set $D_1, ..., D_m$ of real diagonal matrices N by N and Hermitian matrix $A$ of the same size. I am trying to calculate $$\prod_{i=1}^m AD_i$$ Intuitively it seems there should be a way to exploit this structure to make calculations much quicker than O($mN^3$). I know Strassen algorithm would improve this, but it wouldn't use the structure this product has.