Implement an AVL tree$-$based indexing system for a large database of documents. Discuss and design a strategy for efficiently updating and balancing the AVL tree as new documents are added or removed from the database. Consider scenarios such as bulk insertions, deletions, and updates, and analyze the potential impact on the tree's balance factor and overall structure. Additionally, propose techniques for optimizing search operations within the AVL tree to ensure fast retrieval of documents based on various search criteria. Finally, explore advanced topics such as self$-$balancing strategies, node rotation optimizations, and concurrency control mechanisms to enhance the scalability and performance of your AVL tree$-$based indexing system. I want pseudcode and c program