Arbitrage

Arbitrage is the use of discrepancies in currency exchange rates to turn 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 pound, 1 British pound buys 10.0 French francs, and 1 French franc buys 0.21 US dollar. Then, by converting currencies in turn, a clever trader can start with 1 US dollar and end up with $0.5 \times 10.0 \times 0.21 = 1.05$ US dollars, making a 5 percent profit.

Write a program that reads a list of currency exchange rates and determines whether such arbitrage is possible.

The input contains one or more test cases. The first line of each test case has an integer $n$ ($1 \le n \le 30$), the number of different currencies. The next $n$ lines each give the name of one currency; a name contains no spaces. The next line contains an integer $m$, the length of the exchange-rate table that follows. Each of the next $m$ lines contains the name $c_i$ of a source currency, a real number $r_{ij}$ giving the exchange rate from $c_i$ to $c_j$, and the name $c_j$ of the destination currency. Any exchange that does not appear in the table is impossible.

Test cases are separated by a blank line. The input ends with a line containing a single $0$ for $n$.

For each test case, print one line. If arbitrage is possible, print it in the format "Case $c$: Yes"; otherwise print "Case $c$: No". Here $c$ is the test case number, starting from 1.