Multi-Level Inventory Storage with Expiration and Retrieval Priority

Problem: Multi-Level Inventory Storage System Implement an InventorySystem class that supports initialization, storing items, and retrieving items. The warehouse has N levels, numbered from 0 to N - 1, where level 0 is the top level. Each level has the same weight capacity capacity. Each item contains: item_id: a globally unique string; level: the level where the item should be stored; weight: a positive integer weight; timestamp: the time when the item is stored; ttl: time-to-live. The item is considered expired at time timestamp + ttl and afterwards. Implement: class InventorySystem: def __init__(self, n: int, capacity: int): pass def store(self, item_id: str, level: int, weight: int, timestamp: int, ttl: int) -> bool: pass def retrieve(self, timestamp: int) -> str: pass store Rules When calling store(item_id, level, weight, timestamp, ttl): Before the operation, remove all items that are already expired at timestamp; If level is out of range, return False; If an active item with the same item_id already exists, return False; If the target level does not have enough remaining capacity, return False; Otherwise, store the item in the specified level and return True. retrieve Rules When calling retrieve(timestamp): Before the operation, remove all items that are already expired at timestamp; Scan levels from top to bottom, i.e. from 0 to N - 1; A level is eligible for retrieval only if its remaining capacity is at least 50% of its total capacity; From the first eligible level that contains non-expired items, retrieve the item with the largest weight; If multiple items have the same weight, choose the one with the earlier timestamp; if still tied, choose the lexicographically smaller item_id; Remove the retrieved item from the system and return its item_id; If no item can be retrieved, return "EMPTY". Input Format For judging purposes, the input is a sequence of commands: n capacity q command_1 command_2 ... command_q Commands are one of: STORE item_id level weight timestamp ttl RETRIEVE timestamp Output Format Print one line for each command: For STORE, print STORED if successful, otherwise print REJECTED; For RETRIEVE, print the retrieved item_id, or EMPTY if none exists. Constraints 1 <= n <= 10^3 1 <= capacity <= 10^9 1 <= q <= 2 * 10^5 1 <= weight <= capacity 1 <= ttl <= 10^9 Command timestamps are non-decreasing item_id contains only letters, digits, and underscores, and has length at most 32 Example Input: 2 100 5 STORE A 0 30 0 10 STORE B 0 20 1 10 RETRIEVE 2 RETRIEVE 3 RETRIEVE 12 Output: STORED STORED A B EMPTY Example Input 2 100 5 STORE A 0 30 0 10 STORE B 0 20 1 10 RETRIEVE 2 RETRIEVE 3 RETRIEVE 12 Output STORED STORED A B EMPTY