Design an in-memory cloud file system

## In-Memory Cloud File System (OOD) Design an in-memory cloud file system that supports files owned by users with storage quotas. ### Data model / rules - Each file has a unique `name` (string) and a `size` (positive integer). - Each file is owned by exactly one user. - Each user has a **remaining capacity** (how many bytes they can still store). - Special user `"admin"` exists and has **infinite** capacity. - Adding a file consumes the owner’s remaining capacity by `size`. - Deleting a file refunds its size back to the owner’s remaining capacity. ### API to implement Implement a class with the following methods (exact names not required, behavior is): 1. `add_user(user_id, capacity) -> bool` - Create a new user with the given remaining capacity. - Return `false` if the user already exists. 2. `add_file(name, size) -> bool` - Convenience method: add a file owned by `admin`. - Return `false` if the file already exists. 3. `add_file_by(user_id, name, size) -> int | null` - Add a file owned by `user_id`. - Return the user’s **remaining capacity after** adding. - Return `null` if: - `user_id` does not exist - `name` already exists - `size` exceeds the user’s remaining capacity 4. `get_file_size(name) -> int | null` - Return the file size, or `null` if not found. 5. `delete_file(name) -> int | null` - Delete the file. - Return the deleted file’s size, or `null` if not found. 6. `get_n_largest(prefix, n) -> list<string>` - Consider only file names starting with `prefix`. - Return up to `n` files formatted as: `"<name>(<size>)"`. - Sort by: 1) size descending 2) name ascending (lexicographic) for ties 7. `merge_user(user_id_1, user_id_2) -> int | null` - Merge `user_id_2` into `user_id_1`. - All files owned by `user_id_2` become owned by `user_id_1`. - `user_id_1`’s remaining capacity increases by `user_id_2`’s remaining capacity. - Delete `user_id_2`. - Return `user_id_1`’s new remaining capacity. - Return `null` if either user doesn’t exist or the IDs are the same. 8. `backup_user(user_id) -> int | null` - Store a snapshot of the *current set of files owned by* `user_id` (name -> size). - Return the number of files included in this backup. - Return `null` if the user doesn’t exist. 9. `restore_user(user_id) -> int | null` - Restore `user_id`’s files from the most recent backup for that user. - First, remove all files currently owned by `user_id`. - Then, for each file in the backup, restore it **only if its name is not currently used** by some other user. - Return the number of files actually restored. - If the user exists but has no backup, return `0`. - If the user doesn’t exist, return `null`. ### Notes - Assume up to ~1e5 operations. - You may choose any internal data structures, but must satisfy the behavior above.