How to solve a java problem with regular expressions?

Question

Java

The task itself:
Use a regular expression that determines whether the given string is a hexadecimal color identifier in HTML, but is not white (#FFFFFF) or black (#000000).
example of matches: #FFFFF1, #FF3421, #00ff00.
example of inconsistencies: 232323, f#fddee, #fd2, #ffffff.
About the second part of the task (with #FFFFFF and #000000), Google did not give any information. The task does not seem difficult, but I'm at an impasse.
I made this line:

Pattern regex = Pattern.compile("#((([\\dA-Fa-f]){6}))");

Tried to do like this:

Pattern regex = Pattern.compile("#((([\\dA-Fa-f]){6})&&[^(000000)] &&[^(ffffff)])");

But in this case, all entered expressions become false.

Answer 1

~#[a-f\d]{6}(?<!#f{6}|0{6})~i