Autocomplete System

You are building an autocomplete system for a text editor. Implement a Trie that supports adding words and retrieving autocompleted words based on a given prefix. Implement the following methods: 1. `add_word(word: str)` - adds a new word to the trie. 2. `autocomplete(prefix: str) -> List[str]` - returns a list of all words that start with the given prefix in lexicographical order. Input format: - The first line contains an integer, N (1 ≤ N ≤ 1000), the number of operations. - The following N lines contain operations in the format: - `add <word>` (where <word> contains lowercase letters only), - `autocomplete <prefix>` (where <prefix> contains lowercase letters only). Output format: - For each `autocomplete` operation, print the list of matched words on a new line, separated by spaces, or '[]' if no matches found. Example: Input: 4 add apple add application add apply autocomplete app autocomplete a Output: apple application apply a