Longest Nap

The Problem

As you may already know, there are professors who are very busy with a filled schedule of work during the day. Your professor, let's call him Professor P, is a bit lazy and wants to take a nap during the day, but as his schedule is very busy, he doesn't have many chances to do this. He would REALLY like, however, to take one nap every day. Because he'll take just one nap, he wants to take the longest nap that is possible given his schedule. He decided to write a program to help him in this task but, as we said, Professor P is very lazy. Therefore, he finally decided that YOU must write the program!

The Input (nap.in)

The input will consist of an arbitrary number of test cases. Each test case represents one day. The first line of each set contains a positive integer s (not greater than 100) representing the number of scheduled appointments during that day. In the next s lines appear the appointments in the following format:

time1 time2 appointment
time1 represents the time when the appointment starts and time2 the time when it ends. All times will be in the hh:mm format, time1 will always be strictly less than time2, the two times will be followed by a single space and all times will be greater than or equal to 10:00 and less than or equal to 18:00. The nap must be in this interval as well (i.e. no nap can start before 10:00 or end after 18:00). The appointment can be any sequence of characters, but will always occur on the same line. You can assume that no line will be longer than 255 characters, that 10 ≤ hh ≤ 18 and that 0 ≤ mm < 60. You CAN'T assume, however, that the input will be in any specific order. You must read the input until you reach the end of file.

The Output (nap.out)

For each test case, you must print the following line:

Day #d: the longest nap starts at hh:mm and will last for [H hours and] M minutes.
where d stands for the number of the test case (starting from 1) and hh:mm is the time when the nap can start. To display the duration of the nap, follow these simple rules:
  1. if the total duration X in minutes is less than 60, just print "M minutes", where M = X.
  2. if the total duration X in minutes is greater than or equal to 60, print "H hours and M minutes", where H = X div 60 (integer division, of course) and M = X mod 60.
Notice that you don't have to worry with concordance (i.e. print "1 minutes" or "1 hours" if that is the case). The duration of the nap is calculated by subtracting the beginning time of the nap from the ending time of the nap. For example, if one appointment ends at 14:00 and the next one starts at 14:47, then you have (14:47)-(14:00) = 47 minutes of possible nap.

If there is more than one longest nap with the same duration, print the earliest one. You can assume that there will always be at least one possible nap.

Sample Input

10:00 12:00 Lectures
12:00 13:00 Lunch, like always.
13:00 15:00 Boring lectures...
15:30 17:45 Reading
10:00 12:00 Lectures
12:00 13:00 Lunch, just lunch.
13:00 15:00 Lectures, lectures... oh, no!
16:45 17:45 Reading (to be or not to be?)
10:00 12:00 Lectures, as everyday.
12:00 13:00 Lunch, again!!!
13:00 15:00 Lectures, more lectures!
15:30 17:15 Reading (I love reading, but should I schedule it?)
12:00 13:00 I love lunch! Have you ever noticed it? :)

Sample Output

Day #1: the longest nap starts at 15:00 and will last for 30 minutes.
Day #2: the longest nap starts at 15:00 and will last for 1 hours and 45 minutes.
Day #3: the longest nap starts at 17:15 and will last for 45 minutes.
Day #4: the longest nap starts at 13:00 and will last for 5 hours and 0 minutes.