## Jack of All Trades

Jack Barter is a wheeler-dealer of the highest sort. He'll trade anything for anything, as long as he
gets a good deal. Recently, he wanted to trade some red agate marbles for some goldfishh. Jack's friend
Amanda was willing to trade him 1 goldfish for 2 red agate marbles. But Jack did some more digging
and found another friend Chuck who was willing to trade him 5 plastic shovels for 3 marbles while
Amanda was willing to trade 1 goldfish for 3 plastic shovels. Jack realized that he could get a better
deal going through Chuck (1.8 marbles per goldfish) than by trading his marbles directly to Amanda
(2 marbles per goldfish).

Jack revels in transactions like these, but he limits the number of other people involved in a chain of
transactions to 9 (otherwise things can get a bit out of hand). Normally Jack would use a little program
he wrote to do all the necessary calculations to find the optimal deal, but he recently traded away his
computer for a fine set of ivory-handled toothpicks. So Jack needs your help.

### Input

Input will consist of multiple test cases. The first line of the file will contain an integer *n* indicating
the number of test cases in the file. Each test case will start with a line containing two strings and
a positive integer m <= 50. The first string denotes the items that Jack wants, and the second string
identifis the items Jack is willing to trade. After this will be *m* lines of the form

indicating that some friend of Jack's is willing to trade an amount *a1* of item *name1* for an amount *a2*of
item *name2*. (Note this does not imply the friend is also willing to trade *a2* of item *name2* for *a1*
of item *name1*.) The values of *a1* and *a2* will be positive and <= 20. No person will ever need more than
2^31 - 1 items to compete a successful trade.

### Output

For each test case, output the phrase **Case i**: (where *i* is the case number starting at 1) followed by
the best possible ratio that Jack can obtain. Output the ratio using 5 significant digits, rounded. Follow
this by a single space and then the number of ways that Jack could obtain this ratio.

### Sampe Input

2
goldfish marbles 3
1 goldfish 2 marbles
5 shovels 3 marbles
1 goldfish 3 shovels
this that 4
7 this 2 that
14 this 4 that
7 this 2 theother
1 theother 1 that

### Sample Output

Case 1: 1.8000 1
Case 2: 0.28571 3

**NOTE:** problem B from 2008 East Central Regional Contest.