The Peterson Problem
--------------------

Oscar Peterson, one of the greatest jazz musicians of all time,
recently passed away.  He was an adjunct professor in York University's
department of music and he was York's Chancellor from 1991 to 1994.
He was known for dazzling fingerwork on the piano.  In fact, Louis
Armstrong called him "the man with four hands".  In this problem, we
will compute how much his fingers moved when playing songs.

A standard piano keyboard has a linear arrangement of 88 keys.
Musicians, being less logical than computer scientists, did not name
the keys 1,2,3,...,88.  Instead, the keys are grouped into octaves.
Each octave has 12 keys in the following order (from left to right):
C C# D D# E F F# G G# A A# B.  To the right of the B key is the C key
of the next octave.  The keys are coloured black and white.  The black
keys have #'s in their names and the white keys do not.
 
The octaves are numbered:  at the left end of the piano is a partial
octave of 3 keys labelled A0, A#0, B0.  The next octave to the right
is octave 1 (with keys labelled C1, C#1, D1, ..., B1).  The next
octave to the right is octave 2, and so on.  The rightmost complete
octave is octave 7.  Then there is one key (C8) of the next octave.

To add to the confusion, there are alternate names for each of the
black keys:  in any name, the following replacements are possible C# =
Db, D# = Eb, F# = Gb, G# = Ab and A# = Bb.

Suppose Mr Peterson's fingers are numbered 1 to 10 (1 = left pinky, 2
= left ring finger, ..., 5 = left thumb, 6 = right thumb, ..., 10 =
right pinky).  Then each keypress can be specified by a list as
follows.  First we specify a duration (in milliseconds).  Then we
specify how many keys are to be pressed simultaneously.  This is
followed by a list of pairs, where the first number in each pair gives
the finger number and the second number gives the key name.  For
example,

100 3 6 C5 7 E5 9 G5

represents playing a C-major chord of duration 100 milliseconds with
the right hand.  (Three keys are pressed simultaneously for this).
Similarly 

200 3 2 D2 4 F#2 5 A2

represents playing a D-major chord of duration 200 milliseconds with
the left hand.  You may assume that, within each line, the fingers are
listed in increasing order and the keys are also listed from left to
right.  (The latter condition means Mr Peterson will not cross his
fingers or hands while playing.)

A complete song can be expressed by a sequence of lines, where each
line describes a keypress.  The duration on each line indicates how
long to wait after hitting the keys described by that line until
hitting the keys described on the next line.

Note:  there may be some lines that contain only a duration followed
by a 0.  This means the list of keys to press is empty, indicating a
"rest" during which no notes are sounded. 

Assume that any finger hitting a key does so in the exact centre of
the key.  Adjacent white keys have centres 1 inch apart.  The centre
of a white key is half an inch away from the centre of an adjacent
black key. 

To complete a description of where all the fingers are, we have to
know where the fingers that do not participate in a keypress go.  If
there are two fingers f1 and f2 on a hand that participate in the
keypress, then the fingers between f1 and f2 move to locations that
are equally spaced between the locations of f1 and f2.  Fingers to the
right of the rightmost finger that participates in a keypress move to
locations that are spaced at half-inch intervals beyond the rightmost
finger.  Similarly for the fingers to the left of the leftmost finger.
For example, if we have the following description of a keypress:

100 4 1 C2 2 E2 7 C5 10 G5

then 
- finger 3 will be half an inch to the right of finger 2
- finger 4 will be half an inch to the right of finger 3
- finger 5 will be half an inch to the right of finger 4
- finger 6 will be half an inch to the left of finger 7
- fingers 8 and 9 will be 1/3 and 2/3 of the way between fingers 7 and
10 (i.e. finger 8 will be 4/3 inches to the right of finger 7 and
finger 9 will be 4/3 inches to the right of finger 8).

Given a description of a song, you have to compute the total distance
travelled by each finger.  You may assume Mr Peterson's fingers
start at the first position they will play so there is not travelling
required to reach the first keypress.  If one hand is not used during
a keypress, then it just stays where it was.

The input will consist of several instances (songs).  The end of a
song is indicated by a line that contains only 0.  The end of the
input is indicated by a line containing only -1.
See the sample output for the format you should use.
Distances should be accurate to the closest 1000th of an inch.

Sample Input
------------
100 1 1 C4
100 0
200 2 1 D4 4 F#4 
0
100 2 2 C3 5 E3
150 1 3 C4
50 1 8 Eb7
120 2 4 D1 7 F7
100 2 6 C5 10 D#7
200 10 1 C1 2 F#1 3 G1 4 A#1 5 D#2 6 D5 7 F5 8 F#5 9 Bb5 10 C6  
0
-1

Sample Output
-------------
During song number 1:
finger 1 travelled 1 inch.
finger 2 travelled 1.333 inches.
finger 3 travelled 1.667 inches.
finger 4 travelled 2 inches.
finger 5 travelled 2 inches.
finger 6 travelled 0 inches.
finger 7 travelled 0 inches.
finger 8 travelled 0 inches.
finger 9 travelled 0 inches.
finger 10 travelled 0 inches.
During song number 2:
finger 1 travelled 27.5 inches.
finger 2 travelled 30.5 inches.
finger 3 travelled 30.333 inches.
finger 4 travelled 31.167 inches.
finger 5 travelled 33.5 inches.
finger 6 travelled 19.5 inches.
finger 7 travelled 16 inches.
finger 8 travelled 16 inches.
finger 9 travelled 14.5 inches.
finger 10 travelled 13.5 inches.