Every one own herself hero. The different hero must be famous in different field. So to compare them is a difficult things. Now given every hero a integer value to express the degree of famous. We call it Fv.
yifenfei want to know who is the most famous hero, so he ask many people to get the answer. Lots of people tell him as that: the Fv of hero A / the Fv of hero B equal to p / q.
There are multiple cases in the input file.
Each case contains n (0< n <=27)
Next follow n line, each line as (hero A name # hero B name, p , q ).Length of name less 100 (the name will no ”#”). p, q is A positive integer less 10.
Out put every hero relative value, the answer should be smallest(order by the lexicographically of hero name). Out put a line after every case. You may sure every case has answer.
Zhao yun # ji yuan 4 6
Ji yuan # Lemon 3 5
Lemon # Qi shi wang 2 9
Zhao yun 2
ji yuan 3
Ji yuan 6
Qi shi wang 45