Maximum Simultaneous User Sessions

You are given a log with multiple entries. Each entry has a timestamp in hh:mm:ss format, a user ID, and an action which can either be login or logout. For each user, a session starts at login and ends at logout. The log entries may not be in chronological order and events that occur at the same time must be handled by processing the login event before the logout event.

Your task is to compute the maximum number of simultaneous (overlapping) sessions any single user has had.

Note: When two events have the same timestamp, consider the login to occur before the logout to ensure the maximum count is properly recorded.

inputFormat

The first line contains an integer \(n\), representing the number of log entries.

Each of the next \(n\) lines contains a log entry in the format:

hh:mm:ss user_id action

where user_id is an integer and action is either "login" or "logout".

outputFormat

Output a single integer representing the maximum number of overlapping sessions that any user had.

6
12:01:00 1 login
12:05:00 1 logout
12:02:00 2 login
12:06:00 2 logout
12:03:00 1 login
12:07:00 1 logout

2