ARBITRAG  Arbitrage
Arbitrage is the use of discrepancies in currency exchange rates to transform one unit of a currency into more than one unit of the same currency. For example, suppose that 1 US Dollar buys 0.5 British pounds, 1 British pound buys 10.0 French francs, and 1 French franc buys 0.21 US dollars. Then, by converting currencies, a clever trader can start with 1 US dollar and buy 0.5 * 10.0 * 0.21 = 1.05 US dollars, making a profit of 5 percent.
Your job is to write a program that takes a list of currency exchange rates as input and then determines whether arbitrage is possible or not.
Input
The input file will contain one or more test cases. On the first line of each test case there is an integer n (1<=n<=30), representing the number of different currencies. The next n lines each contain the name of one currency. Within a name no spaces will appear. The next line contains one integer m, representing the length of the table to follow. The last m lines each contain the name c_{i} of a source currency, a real number r_{ij} which represents the exchange rate from c_{i} to c_{j} and a name c_{j} of the destination currency. Exchanges which do not appear in the table are impossible.
Test cases are separated from each other by a blank line. Input is terminated by a value of zero (0) for n.
Output
For each test case, print one line telling whether arbitrage is possible or not in the format "Case case: Yes", respectively "Case case: No".
Example
Input:3 USDollar BritishPound FrenchFranc 3 USDollar 0.5 BritishPound BritishPound 10.0 FrenchFranc FrenchFranc 0.21 USDollar 3 USDollar BritishPound FrenchFranc 6 USDollar 0.5 BritishPound USDollar 4.9 FrenchFranc BritishPound 10.0 FrenchFranc BritishPound 1.99 USDollar FrenchFranc 0.09 BritishPound FrenchFranc 0.19 USDollar 0Output:Case 1: Yes Case 2: No
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bhaduriu:
20170419 17:45:17
BellmanFord Algorithm, using negative logarithmic edges and then detecting a negative cycle. Done! 

vengatesh15:
20170214 20:32:17
AC in 1 go using Floyd warshall.. 

hackerman97:
20170102 15:58:06
Space after semicolon : : 

deerishi:
20161102 17:52:25
Awesome Problem! Cool application of Floyd Warshall. 

gustavoaca1997:
20160901 10:00:37
input:


PKJ:
20160620 17:18:27
3


Shubham Garg:
20160102 20:12:47
@Dimitris  double works 

Dimitris Rontogiannis:
20150912 17:34:13
Be careful, double gives WA.


Praveen Kulkarni:
20150627 16:46:28
@eightnoteeight my AC solution gives No


Ankit Sultana:
20150608 22:17:22
There are indeed cases with conversion of the form Currency Rate Currency 
Added by:  Vincenzo Bonifaci 
Date:  20110807 
Time limit:  0.242s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  University of Ulm Local Contest 1996 