Calculate Courier Earnings

Design a function to calculate total courier pay from a set of delivery orders. Assume time is represented as integer minutes, and intervals are half-open: an order active from minute `start` to minute `end` contributes on `[start, end)`. ### Base version Each order has: - `accepted_at` - `delivered_at` There is a global `rate` paid per minute. For any minute in which an order is active, that order earns `rate * k`, where `k` is the number of orders active in that same minute. In other words, if `k` orders overlap during a minute, the total pay contributed by that minute is `k * k * rate`. Implement a function that returns the total pay across all orders. The interviewer may ask you to define reasonable input/output structures yourself, explain your chosen data structures, analyze time and space complexity, and write meaningful test cases. ### Follow-up 1 Now each order may also include: - `arrived_at` - `picked_up_at` The interval `[arrived_at, picked_up_at)` is store-wait time. A store-wait minute is paid only for that order itself: - it must not increase the multiplier for any other order - other orders must not increase its multiplier Update the design to support this rule. ### Follow-up 2 During configurable peak-hour intervals, the per-minute rate is doubled. Explain how you would extend your solution to support this efficiently.