Maximum Team Size from Overlapping Availability

# Maximum Team Size from Overlapping Availability You are given two arrays, `startTime` and `endTime`, each of length `n`. Employee `i` is available throughout the closed interval `[startTime[i], endTime[i]]`. Two employees can interact when their intervals share at least one time point. A team is valid if at least one employee in that team can interact with every other member. Return the largest possible size of a valid team. Other pairs of team members need not overlap, and there need not be one time point shared by the entire team. ### Function `int maximumTeamSize(vector<int>& startTime, vector<int>& endTime)` ### Example 1 **Input:** `startTime = [2, 0, 6, 11], endTime = [8, 2, 6, 12]` **Output:** `3` **Explanation:** The employee with interval `[2, 8]` can interact with the employees available during `[0, 2]` and `[6, 6]`. These three employees form a valid team even though the latter two intervals do not overlap. The employee available during `[11, 12]` cannot join that team. ### Example 2 **Input:** `startTime = [5, 5, 8], endTime = [5, 7, 9]` **Output:** `2` **Explanation:** The first two employees can interact at time `5`, so they form a team of size `2`. The interval `[8, 9]` is disjoint from both of their intervals. ### Constraints - `1 <= n == startTime.length == endTime.length <= 100000` - `0 <= startTime[i] <= endTime[i] <= 1000000000` ### Clarifications - Touching at an endpoint counts as overlap. - A zero-length interval `[t, t]` is allowed. - The employee who overlaps everyone else is included in the team size. ### What a Strong Answer Covers - Applying the one-employee interaction requirement rather than requiring every pair to interact. - Handling equal endpoints, duplicate intervals and zero-length intervals correctly. - Supporting all `100000` employees without checking every pair separately.