Compute max simultaneous drivers last 24 hours

Given delivery intervals (driverId, startTime, endTime) already recorded, implement maxSimultaneousDriverInPast24Hours() that returns the maximum number of distinct drivers who were simultaneously on a delivery at any instant within the window (now−24h, now]. Precisely define "simultaneous" and the interval semantics (open/closed). If multiple times achieve the maximum, optionally also return one such timestamp or the corresponding maximal intervals. Describe an efficient algorithm and data structures that support online inserts from RecordDelivery and queries with strong performance guarantees, and analyze time and space complexity.