Moving parts of a filename

I have a bunch of music files that I'd like to rearrange the names of.
Currently they are ARTIST(.)FILENUMBER( )FILENAME.mp3
I'd like them to be FILENUMBER(.)ARTIST(.)FILENAME.mp3
eg
Deigen.20 Cosmic Upside Down.mp3
should be
20.Deigen.Cosmic Upside Down.mp3
and
KAWAGUCHI MASAMI NEW ROCK SYNDICATE.09 DAN DAN.mp3
should be
09.KAWAGUCHI MASAMI NEW ROCK SYNDICATE.DAN DAN.mp3

The first dot separates the ARTIST and FILENUMBER and the third character after that is the start of the FILENAME.

I don't know much about regex

TIA

I worked it out

Replace: (.*)\.(\d*)(.)(.*)
with: \2.\1.\4
Use regular expressions

It gets the job done. Is there a simpler way?