Redirect all requests to HTTPS AND www to non-www - apache

Question

I'm fixing my Apache (2.4.12) config files on a server that serves three different domain names. I have a different config file for each site. I cannot for the life of me figure out how to accomplish both of the following:
Redirect all http requests to https, keeping the entire rest of the request (subdomain/host AND document path) exactly the same
Redirect all www requests to non-www
I've read that this can be done in one step if I have only one *:80 VirtualHost and put the rewrite rules there (the remainder of my subdomains are all *:443 VirtualHosts with the exception of www), but I can't figure out how to do it. These answers on SO did not work:
The accepted answer in this question is not correct (only does the https redirect)
This answer does not work for me--only the https redirect works.
This question doesn't deal with a wildcard subdomain and is thus inapplicable.
This question is also inapplicable because it doesn't deal with subdomains.
EDIT: This is the code I reference in the comments for mike.k's answer below.
<VirtualHost *:80>
RewriteEngine On
RewriteCond %{HTTP_HOST} www.example.com
RewriteRule ^(.*)$ https://example.com/$1 [R=permanent,L]
RewriteCond %{HTTPS} off
RewriteRule (.*) https://example.com%{REQUEST_URI}
</VirtualHost>

Answer 1

This is from my production system and works.
THE_HOSTNAME is for instance server, and then THE_FQHN is server.domain.edu, which helps for SSL certificates if you don't want to support wildcards and multiple domain names.
# redirect to FQHN
RewriteEngine on
RewriteCond %{HTTP_HOST} THE_HOSTNAME$
RewriteRule ^(.*)$ https://THE_FQHN/ $1 [R=permanent,L]
# redirect to HTTPS
RewriteCond %{HTTPS} off
RewriteRule (.*) https://THE_FQHN%{REQUEST_URI}
In your case www.domain.com would be where THE_HOSTNAME is, and THE_FQHN would be domain.com, just flipped around