Compute minimum meeting rooms on circular day

## Problem You are given a list of meetings scheduled within a 24-hour day. Time is **cyclic**: after `23:59` the next minute is `00:00`. Each meeting is represented as `(start, end)` where `start` and `end` are times within the day (e.g., minutes from `0` to `1439`, or strings `HH:MM` you can convert to minutes). - A meeting occupies the half-open interval **[start, end)**. - If `end > start`, the meeting occurs within the same day. - If `end <= start`, the meeting **wraps past midnight** (e.g., `23:00 -> 01:00`). Two meetings overlap if their occupied time intervals intersect (considering wrap-around). ### Task Return the **minimum number of conference rooms** required so that no overlapping meetings share a room. ### Examples - Meetings: `[(60, 120), (90, 150)]` → overlaps → answer `2`. - Meetings: `[(1380, 60), (30, 90)]` where `(1380, 60)` wraps midnight → overlaps with `(30, 90)` → answer `2`. ### Constraints - `1 <= n <= 2 * 10^5` - Times are within one day (0..1439) or equivalent. ### Follow-up If the number of meetings is extremely large, how would you optimize the approach (time and/or space), given the timeline is only one day and thus bounded?