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BIG-Bench Extra Hard (BBEH) / Sarah, Charlotte and Yolanda work from 9 to 5 their local time on weekdays. They…

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input

Sarah, Charlotte and Yolanda work from 9 to 5 their local time on weekdays. They want to have a meeting some time this week.

The schedule for Sarah's week in their local time is as follows:
Monday: Free only at the following times: anytime before 10:15, from 11:20 to 11:25, from 12:55 to 17:00
Tuesday: Free only at the following times: from 9:40 to 9:40, from 10:20 to 10:30, from 11:55 to 17:00
Wednesday: Free only at the following times: from 9:00 to 9:35, from 10:40 to 11:45, from 12:45 to 14:10, from 14:15 to 14:40, anytime after 16:10
Thursday: Booked at the following times: from 9:30 to 9:50, from 10:05 to 11:30
Friday: Free only at the following times: from 9:00 to 10:15, from 10:35 to 11:15, from 12:20 to 12:25, from 13:10 to 13:25, anytime after 14:20


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


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


Sarah is flexible to miss the last (at most) 10 minutes of the meeting
Charlotte can clear any meeting of 30 minutes or less from their schedule to accommodate the meeting
Yolanda needs a break for lunch on Wednesday from 12:30 to 1:00
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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