Unit Calculator
---- ----------

You have been asked to write a program that will perform
context dependent unit conversions.   For example, if
you are selling apples and oranges and want to know
how many oranges you must sell to generate as much
revenue as selling 1 apple, you could give the program:

	12 apples = 4.95 dollars
	12 oranges = 3.25 dollars
	1 apples = ? oranges

to which the answer is:

	1 apples = 1.523 oranges

Similarly if you want to know how many kilowatts of
energy it takes to heat 1 gallon of water 60 degrees
Fahrenheit in 1 minute, you could give the program:

	1 BTUs = 1 degrees-F pounds
	1 BTUs = 1055 joules
	1 joules = 1 watts seconds
	1000 watts = 1 kilowatts
	60 seconds = 1 minutes
	1 gallons = 8.3454 pounds
	60 degrees-F gallons = ? kilowatts minutes

to which the answer is

	60 degrees-F gallons = 8.804 kilowatts minutes

Notice the first problem makes apples and oranges
equivalent to dollars, which only works in a particular
context.  The second problem makes 1 gallon equal to
8.3454 pounds, and 1 BTU equal to 1 degrees-F per
pound, and these equations work only for water.  So
our problems are context sensitive.

To simplify things we always use the plural for unit
names, thus writing such syntactic barbarisms as 
`1 apples'.  The lexemes are

    <number> ::= any number readable as floating point
    <unit-name> ::= sequence of graphic characters
                    that begins with a letter
    <special> ::= / | = | ? | .

A `graphic' character is a character that prints a mark.
Lexemes are always separated from each other by white-
space.

There is one statement per input line.  The statement
syntax is:

    <units> ::= <unit-name>* <divisor>*
    <divisor> ::= / <unit-name>
    <quantity> ::= <number> <units>
    <equivalence> ::= <quantity> = <quantity>
    <query> ::= <quantity> = ? <units>
    <end> ::= .
    <statement> ::= <equivalence> | <query> | <end>

Input 
-----

For each of several test cases, a line containing just a
test case name, followed by lines containing equiva-
lences used in the calculation, followed by lines con-
taining queries, followed by a line containing just `.'.
Note that there can be more than one query, and lines
and unit names can be long.

All input is lexically and syntactically legal.  All
numbers input are > 0.

There are at most 100 distinct <unit-name>s in a test
case and at most 100 <equivalence>s.  In all test cases
there will be at most 1,000 <query>s.

Input ends with an end of file.


Output
------

For each test case, first a line containing an exact
copy of the test case name line, and for each input
query line an exact copy of that line but with the ?
replaced by a number with exactly 3 decimal places.
Input will be such that every query will have a unique
answer.


Sample Input
------ -----

-- APPLES AND ORANGES --
12 apples = 4.95 dollars
12 oranges = 3.25 dollars
1 apples = ? oranges
.
-- HEATING WATER --
1 BTUs = 1 degrees-F pounds
1 BTUs = 1055 joules
1 joules = 1 watts seconds
1000 watts = 1 kilowatts
60 seconds = 1 minutes
1 gallons = 8.3454 pounds
1 BTUs = ? kilowatts minutes
60 degrees-F gallons = ? BTUs
60 degrees-F gallons = ? kilowatts minutes
.
-- STRANGE --
5 / X = 7
3 X = ?
.


Sample Output
------ ------

-- APPLES AND ORANGES --
1 apples = 1.523 oranges
-- HEATING WATER --
1 BTUs = 0.018 kilowatts minutes
60 degrees-F gallons = 500.724 BTUs
60 degrees-F gallons = 8.804 kilowatts minutes
-- STRANGE --
3 X = 2.143


File:	   unitcalc.txt
Author:	   Bob Walton <walton@seas.harvard.edu>
Date:	   Wed Oct 15 07:28:20 EDT 2014

The authors have placed this file in the public domain;
they make no warranty and accept no liability for this
file.

RCS Info (may not be true date or author):

    $Author: walton $
    $Date: 2014/10/15 11:29:46 $
    $RCSfile: unitcalc.txt,v $
    $Revision: 1.10 $