I need a clean, modern Flutter app that lets users exchange text messages in real time. Every user who signs up should instantly appear in a single public chat—no contact selection or private rooms. Core requirements are straightforward: • Firebase Authentication handles sign-up and login. • Messages live in Cloud Firestore and update instantly across devices. • Each user can edit or delete only their own messages. • UI stays simple, responsive, and visually consistent with current Flutter Material 3 guidelines. Deliverables • Complete, well-structured Flutter source code (Dart). • Firebase project configuration for Auth and Firestore. • A concise setup guide so I can run the project locally and deploy it to both Android and iOS. Keep the code clean, comment where it matters, and avoid unnecessary packages; Firebase core, auth, and cloud_firestore should cover it. If anything in the brief seems unclear, let me know early so we can keep the build cycle tight and efficient.