Implement a calendar with non-overlapping bookings

## Problem Design a calendar booking system that stores half-open time intervals `[start, end)` (inclusive of `start`, exclusive of `end`). Implement a class with a method: - `book(start, end) -> boolean` The method should: - Return `true` and add the event if it does **not** overlap with any existing event. - Return `false` and do **not** add the event if it overlaps with an existing event. Two events `[s1, e1)` and `[s2, e2)` overlap iff `max(s1, s2) < min(e1, e2)`. ### Example Operations: - `book(10, 20)` → `true` - `book(15, 25)` → `false` (overlaps with `[10,20)`) - `book(20, 30)` → `true` (touching at 20 is allowed) ### Constraints (typical) - Up to `10^3` to `10^5` bookings - `0 <= start < end <= 10^9`