Script to add all mailbox sizes per database

I'm looking for a script that will do two things:

1. Show total number of mailboxes per database
2. Show actual total size of all mailboxes per database added together

I can runGet-Mailbox | Group-Object -Property:Database | select name,count and that will give me the total number of mailboxes per database. I can run Get-MailboxDatabase -Status | ft name,databasesize, but that gives me the white space also which I don't want. For example…I have a database that is 135 GB in size, but if I export aGet-MailboxStatistics and add the totalitemsize for all mailboxes, the real total is closer to 70 GB.

So the output I'm looking would include database name, number of mailboxes per database, and the size of all mailboxes (from the totalitemsize field) added together per database.

Really appreciate any help. Thanks

~Rick