Getting There

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

 A frustrating part of arranging your own air travel trip is selecting from among many possible flights that sequence of flights which will take you from your origin to your destination in the least possible time or for the least possible cost.


It should be clear to any frequent air passenger that in order to reach one city from another, the cost of the shorter flight may be more than the cost of longer flights. In other words, it may pay you well to cool your heels in an airport waiting for a connecting flight rather than take a more direct flight or one in which the connecting time is shorter. For example, consider the following flight schedule.


            Center City     Homeville       5:2OA  6:55A  12.50
            Center City     Greenville      5:45A  9:l5A  35.00
            Homeville       Greenville      7:45A  9:35A  20.00

In order to travel from Center City to Greenville, you have two choices. You can travel from Center City to Homeville, then from Homeville to Greenville, or you can travel directly from Center City to Greenville. The first route costs $32.50 and has travel time 4:15; the direct route costs $35.00 and has travel time 3:30. If minimizing cost is your objective, then you would choose the first route. If you want to minimize time, you would select the second route.


You are to write a program to optimize route selection given the criteria of least cost or least time. Your program will read a list of flights and several trip rcquests and will select from the list of flights the best sequence to satisfy each trip request. For each request, if more than one route should satisfy the request, then your program should select the route that also satisfies the other objective. For example, if cost is to be minimizad and if two routes both yield the minimum cost, then select the route which yields the shortest travel time. If two routes yield identical costs and travel times, then select either route. 


 The input consists of several blocks. First line contains number of these blocks. Every block is broken into two segments, the first describing the list of flights and the second containing the trip requests. The end of each segment is indicated by the line consisting of the single character `#'.


The flight segment of the file describes individual flights, one per line. Each line contains the origin city (columns 1 through 19), the destination city (columns 21 through 39), the departure time (columns 41 through 46). the arrival time (columns 48 through 53), and the cost (columns 55 through 60). City names are left-justified in their respective fields, and may contain upper and lower case characters and spaces. Times are in the form HH:MMX, where HH is the hour (a leading zero may be replaced by a blank), MM is the minutes (exactly two digits will appear), and X is A (for AM), P (for PM), or M or N (this can be used only after 12:00 to distinguish midnight from noon). The cost of the ticket is in dollars and cents, and includes a decimal point and two fractional digits. No tickets are free or cost more than $999.99. No individual flight represented by a line in the schedule takes more than 24 hours. There will be at most 20 flights on the schedule.


The trip request segment follows the list of flights. Each request appears on a line by itself, and specifies the origin city (columns 1 to 19), the destination city (columns 21 to 39), and whether to optimize cost or travel time. If it is desired to optimize travel time, the word TIME is in columns 41 to 44. If cost is to be optimized, then the word COST is in columns 41 to 44. There may be trailing blanks in any line in the flight schedule or the trip requests. 


 For each travel request, display the request and the optimal route in the form shown below. Notice that trailing spaces are removed from city names. Time is output in the form <hh>:<mm>, where <hh> goes from 0 to 23 and <mm> goes from 0 to 59. If the trip takes more than one day, the time output starts with the number of days and string "day" appended (or "days" if the flight takes more than 48 hours). There are no leading zeroes nor blanks allowed.


All optimum routes will require less than 10 days and less than $1,000.00. Place exactly one blank line between the outputs for successive trips. 

Sample Input

Center City      Homeville        5:2OA 6:55A     12.50
Center City      Greenville       5:45A 9:l5A     35.00
Homeville        Greenville       7:45A 9:35A     20.00
Archer City      Homeville        5:OOA 6:OOP    612.50
Center City      Greenville       COST
Archer City      Greenville       TIME

Sample Output

Center City->Greenville,4:15,32.50
Center City->Homeville,5:20-6:55,12.50

Archer City->Greenville,1 day 4:35,632.50
Archer City->Homeville,5:00-18:00,612.50