Berth occupancy point and range-maximum queries at scale

# Marina berth occupancy queries at scale `input.json` (synthetic) has `bookings` ([start, end) integer minute pairs), `points` (integer times) and `ranges` ([l, r) pairs). Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json`. One hidden input has **150,000 bookings and about 300,000 queries and must finish within 20 seconds** (other runs: 30 s). Answers must be exact. ## Rules 1. A booking with start > end is invalid: count it in `invalid_bookings` and ignore it. A booking with start == end is ignored (not invalid). Duplicate bookings count separately. 2. Occupancy at integer time t = number of valid bookings with start <= t < end. 3. `points`: occupancy at each time, in input order. 4. `ranges`: for each [l, r): if l >= r the answer is null; otherwise the maximum occupancy over all integer t with l <= t < r. In input order. 5. `peak` = maximum occupancy over all times (0 if there are no valid bookings); `peak_first_time` = the earliest time it is reached (null if peak is 0). ## answer.json `{"invalid_bookings", "peak", "peak_first_time", "points": [...], "ranges": [...]}` ## Scoring Hidden checks (partial credit; all must pass; all exact): `invalid_and_peak`, `point_queries`, `range_max_queries` on the given input; `fresh_run_1`, `fresh_run_2`; `big_150k_bookings_300k_queries_20s`.