Design a constrained in-memory file system

Design an in-memory hierarchical file system. Implement:

1. addFile(String path): Given a UNIX-style absolute path like "/path/to/somewhere/file.txt", create intermediate directories as needed and store a file at the final segment.
2. listEntries(String path): Given a directory path, return the names of its immediate children in lexicographic order. For example, after addFile("/path/to/somewhere/file.txt"), listEntries("/path/to/somewhere") -> ["file.txt"], and listEntries("/path/to") -> ["somewhere"]. Constraints: • Each directory may contain at most 5 entries (files or folders). If an insertion would exceed this limit, reject the operation and leave the structure unchanged. • On duplicate name insertion within the same directory, automatically rename the new entry by appending "(k)" before the file extension (if any), where k is the smallest positive integer that yields an unused name. Example sequence in the same directory: addFile("file.txt"), addFile("file.txt"), addFile("file ( 1).txt") results in files named "file.txt", "file ( 1).txt", "file ( 1)( 1).txt". Requirements: Describe your data structures, parsing/extension handling, and the time/space complexity of addFile and listEntries. Discuss edge cases (root path, trailing slashes, invalid paths).