freatevietnam/freateoj ? reverse-engineered prompt

Build me a full online judge site for programming contests, similar to what schools or coding clubs would use. I want users to be able to browse problems, read statements with math formulas rendered nicely, submit code in lots of languages like C, C++, Java, and Python, and get live verdict updates while judging is running.

It should support normal practice mode plus contests, including ICPC style and IOI style scoring, with real time standings, batch rejudging, and problem versioning. Please include dark and light themes, admin tools to manage problems and contests, and a secure judge setup for running submissions safely. If the project already has demo data, wire that up so I can sign in quickly and test everything.

Please get it running locally in a sensible way, use the existing docs and current online docs if you need to, and leave me with a working app plus clear setup notes for things like problem data storage and caching.