Prompt

Please write a high quality, general purpose solution. Implement a solution that works correctly for all valid inputs, not just the test cases. Do not hard-code values or create solutions that only work for specific test inputs. Instead, implement the actual logic that solves the problem generally.

Focus on understanding the problem requirements and implementing the correct algorithm. Tests are there to verify correctness, not to define the solution. Provide a principled implementation that follows best practices and software design principles.

If the task is unreasonable or infeasible, or if any of the tests are incorrect, please tell me. The solution should be robust, maintainable, and extendable.