Modular Hat Rack

I needed a way to organize my hats, and the closest thing that i found that made sense to me was this file https://www.thingiverse.com/thing:1366821
It's really good but I had a couple of ideas to improve it, mainly simplifying it to just ONE file and removing the need of glue to attach every piece, thanks to dovetails.
To mount it on a wall/door, just drive a screw into the wall/door leaving some space for the rack module to hold on to (every module has a slot for a screw).
I have nine modu