Breaking (Is) Bad

Brittany is trying to set up her class schedule for the Fall 2019 semester. Since she is a commuter student, she wants to schedule her classes close to one another so that she can arrive on campus, attend class, and go back home without long breaks between classes.

Given several potential class schedules for one day, Brittany needs to determine the minimum possible total time spent between classes throughout that entire day.

The input begins with a single line containing an integer $n$ ($2 \le n \le 10$). The next $n$ lines each contain a potential schedule for the day. Each schedule consists of at least $1$ and at most $8$ class times, separated by spaces.

Each class time is formatted as `hourStart:minuteStart-hourEnd:minuteEnd`, where
the hours range from $0$–$23$ and the minutes range from
$0$–$59$. A leading zero is included for
single-digit minutes, but there is no leading zero for
single-digit hours. Every class lasts at least $1$ minute, and the number of minutes
between each ending time and the next starting time is always
non-negative. Note that the time between consecutive classes
*can* be zero—Brittany is an accomplished sprinter, so
this doesn’t bother her.

Output a single line containing the minimum possible total
minutes Brittany can have between classes throughout the day.
If any of the potential schedules have only one class, output
`0`.

Sample Input 1 | Sample Output 1 |
---|---|

2 9:00-9:55 10:05-11:30 11:35-12:30 9:10-10:05 10:45-11:45 |
15 |

Sample Input 2 | Sample Output 2 |
---|---|

2 9:40-11:05 9:40-11:05 11:20-12:45 |
0 |