How to compute $\int_{-\infty}^{\infty} (z-w)^{(n/2 - 1)}w^{(n/2 - 1)}\ dw$?

Question

I am trying to integrate: $$ \int_{-\infty}^{\infty} (z-w)^{(n/2 - 1)}(w)^{(n/2 - 1)}\ dw$$ where $n$ is an integer and $z$ is real. I tried repeated integration by parts but wasn't able to reduce this. If anyone could provide a hint I would appreciate it. Thanks!