Minimum Number of Servers for Tasks on a 24-hour Cycle (Wrap-around Allowed)

Problem: Minimum Number of Servers (24-hour cycle, wrap-around allowed) You are given a set of tasks running on servers. Each task is represented by a pair (start, duration): start: the start time in minutes within a day, 0..1439. duration: the running time in minutes (positive), which may exceed 1440, so a task may extend into the next day(s). Once started, a task runs continuously until it finishes. A server can run at most one task at any time. Time is displayed on a 24-hour cycle (mod 1440), but the actual occupation happens on a continuous timeline. Return the minimum number of servers required to run all tasks. Input format (suggested) First line: integer n, number of tasks Next n lines: two integers start duration Output format One integer: the minimum number of servers Constraints 1 <= n <= 2*10^5 0 <= start < 1440 1 <= duration <= 10^9 Example Tasks: (23*60, 60) runs 23:00–24:00 (0, 30) runs 00:00–00:30 (23*60, 30) runs 23:00–23:30 Output: 2 Example Input 3 1380 60 0 30 1380 30 Output 2