Toll

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Sindbad the Sailor sold 66 silver spoons to the Sultan of Samarkand. The selling was quite easy; but
delivering was complicated. The items were transported over land, passing through several towns and
villages. Each town and village demanded an entry toll. There were no tolls for leaving. The toll for entering a
village was simply one item. The toll for entering a town was one piece per 20 items carried. For example, to
enter a town carrying 70 items, you had to pay 4 items as toll. The towns and villages were situated
strategically between rocks, swamps and rivers, so you could not avoid them.

Figure 1: To reach Samarkand with 66 spoons, traveling through a town followed by two villages, you must
start with 76 spoons.

Figure 2: The best route to reach X with 39 spoons, starting from A, is AbcX, shown with arrows
in the figure on the left. The best route to reach X with 10 spoons is ADX, shown in the figure on the
right. The figures display towns as squares and villages as circles.
Predicting the tolls charged in each village or town is quite simple, but finding the best route (the cheapest
route) is a real challenge. The best route depends upon the number of items carried. For numbers up to 20,
villages and towns charge the same. For large numbers of items, it makes sense to avoid towns and travel
through more villages, as illustrated in Figure 2.
You must write a program to solve Sindbad's problem. Given the number of items to be delivered to a certain
town or village and a road map, your program must determine the total number of items required at the
beginning of the journey that uses a cheapest route.
 

Input

The input consists of several test cases. Each test case consists of two parts: the roadmap followed by the
delivery details.
The first line of the roadmap contains an integer n, which is the number of roads in the map (0<=n). Each of
the next n lines contains exactly two letters representing the two endpoints of a road. A capital letter
represents a town; a lower case letter represents a village. Roads can be traveled in either direction.
Following the roadmap is a single line for the delivery details. This line consists of three things: an integer p (
0 < p <= 1000) for the number of items that must be delivered, a letter for the starting place, and a letter for the
place of delivery. The roadmap is always such that the items can be delivered.
The last test case is followed by a line containing the number -1.
 

Output

The output consists of a single line for each test case. Each line displays the case number and the number of
items required at the beginning of the journey. Follow the output format in the example given below.
 

Sample Input

1
a Z
19 a Z
5
A D
D X
A b
b c
c X
39 A X
-1

Sample Output

Case 1: 20
Case 2: 44

Hint

 

Source

Beverly Hills 2002-2003