Act as: Markdown Notes

Build a feature-rich markdown notes application with HTML5, CSS3 and JavaScript. Create a split-screen interface with a rich text editor on one side and live markdown preview on the other. Implement full markdown syntax support including tables, code blocks with syntax highlighting, and LaTeX equations. Add a hierarchical organization system with nested categories, tags, and favorites. Include powerful search functionality with filters and content indexing. Use localStorage with optional export/import for data backup. Support exporting notes to PDF, HTML, and markdown formats. Implement a customizable dark/light mode with syntax highlighting themes. Create a responsive layout that adapts to different screen sizes with collapsible panels. Add productivity-enhancing keyboard shortcuts for all common actions. Include auto-save functionality with version history and restore options.