Formula to extract First initial, Middle initial and Last name from cell

Hello,

I need help creating a formula that extracts a first initial, middle initial and last name from a cell. For example, If A1 contains Jane M. Doe, I'd like to populate the new cell with jmdoe.

So far I have this:

=PROPER(LEFT(A1)&TRIM(RIGHT(SUBSTITUTE(A1," ",REPT(" ",99)),99)))

Which grabs the first initial and last name, but I'm having problems getting the middle initial.

Thank you!