How to programmatically recognize if a font supports Cyrillic?

Question

Java

The task is this - there is a list of all fonts installed on the user's machine. It is necessary to sort it out, leaving only those that support the Cyrillic alphabet.

At the moment, I went through the standard ones with my hands + googled the most used ones. The list turned out to be large, but I still did not solve the problem, because custom fonts often come across on the user's machine.

I'm considering this option - draw a Latin letter and compare it with a square that is drawn if the character is not recognized. I guess how to do it, but I can spend from a week on it.

Are there other ways to do this?