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BIG-Bench Extra Hard (BBEH) / Lisa, Sophia, Nancy and Amelia work from 9 to 5 their local time on weekdays.…

Problem

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input

Lisa, Sophia, Nancy and Amelia work from 9 to 5 their local time on weekdays. They want to have a meeting some time this week.

The schedule for Lisa's week in their local time is as follows:
Monday: Booked at the following times: from 9:50 to 11:15, from 12:25 to 13:20, from 14:20 to 15:35
Tuesday: Booked at the following times: from 9:20 to 9:55, from 11:10 to 12:35
Wednesday: Free only at the following times: anytime before 9:50, from 10:45 to 12:10, from 12:15 to 13:35, from 14:50 to 16:05, from 16:55 to 17:00
Thursday: Free only at the following times: anytime before 10:25, from 10:55 to 11:20, from 12:00 to 17:00
Friday: Booked at the following times: from 10:00 to 10:05, from 10:15 to 11:00, from 12:20 to 12:55, from 14:00 to 15:20


The schedule for Sophia's week in their local time is as follows:
Monday: Booked at the following times: from 9:10 to 10:10, from 11:00 to 11:15
Tuesday: Booked at the following times: from 9:30 to 10:25, from 10:45 to 10:50, from 11:20 to 12:15
Wednesday: Free only at the following times: anytime before 10:00, from 10:15 to 11:10, anytime after 11:30
Thursday: Booked at the following times: anytime before 10:20, from 10:45 to 11:15, from 11:40 to 11:50, from 12:45 to 13:00
Friday: Free only at the following times: anytime before 9:55, from 10:40 to 11:50, anytime after 12:40


The schedule for Nancy's week in their local time is as follows:
Monday: Booked at the following times: from 10:20 to 11:35, from 11:50 to 13:10
Tuesday: Free only at the following times: from 9:00 to 10:00, from 11:10 to 11:15, anytime after 12:00
Wednesday: Free only at the following times: from 9:00 to 9:20, from 9:55 to 10:20, from 11:20 to 11:45, from 13:00 to 14:05, anytime after 14:10
Thursday: Free only at the following times: from 9:00 to 9:30, from 10:50 to 11:15, from 12:45 to 13:50, from 14:30 to 17:00
Friday: Free only at the following times: from 9:00 to 9:20, from 10:40 to 10:40, from 11:25 to 12:10, from 12:40 to 17:00


The schedule for Amelia's week in their local time is as follows:
Monday: Free only at the following times: anytime before 10:00, from 11:05 to 11:30, from 12:05 to 17:00
Tuesday: Booked at the following times: from 9:30 to 9:35, from 9:50 to 10:30, from 11:40 to 13:05
Wednesday: Free only at the following times: anytime before 9:35, from 10:20 to 11:25, from 11:40 to 17:00
Thursday: Booked at the following times: from 9:35 to 10:25, from 10:25 to 11:30
Friday: Free only at the following times: anytime before 9:45, from 10:45 to 11:55, from 12:15 to 12:55, from 13:05 to 13:15, anytime after 14:05


Lisa is flexible to miss (at most) 10 minutes of the meeting
Sophia needs a break for lunch on Wednesday from 12:30 to 1:00
Nancy asks the meeting to be scheduled such that she has at least 10 minutes of free time before the meeting (the free time must fall within her 9am to 5pm)
Amelia is flexible to miss the last (at most) 10 minutes of the meeting
Let X be the length of the longest meeting (in minutes) that can be scheduled if the meeting has to start on the hour or half hour. Also, let Y be number of possible options of such meetings. Compute X and Y and report them separated by a comma (e.g., 45, 3). If X is 0, report 0, 0.

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