Is there a way to redirect a sub folder to no-www?

What I use is:

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} ^www\.(.*)$ [NC]
RewriteRule ^(.*)$ http://%1/$1 [R=301,L]

but this only redirects the www.example.com to example.com.

I would like to redirect:

www.example.com/home/ to example.com/home/

www.example.com/home/whatever URL to example.com/home/whatever URL.

I have tried this:

RewriteEngine on
Options +FollowSymlinks -MultiViews

RewriteCond %{HTTP_HOST} ^(www\.)?example\.com$ [NC]
RewriteRule ^$ http://example.com [R=301,L]

RewriteCond %{HTTP_HOST} ^www\.example\.com$ [NC]
RewriteCond %{REQUEST_URI} !^/home/ [NC]
RewriteRule ^(.+)$ http://example.com/$1 [R=301,L]

This does not work, either. I can't really figure it out. Any help appreciated!

ANSWER

I figured it out and I will post it for others to see, if having the same issue.

In the sub folder directory's .htaccess used the following:

RewriteCond %{HTTP_HOST} ^(www\.example\.com)?$
RewriteRule ^(.*)$ http://example.com/subfoldername/$1 [R=301,L]