Oh, Those Achin' Feet

Time Limit: 2 Seconds
Memory Limit: 65536 KB

In recent days, a number of people have been injured after being pushed off
the sidewalks due to overcrowding. City Hall is interested in figuring out how
much pedestrian traffic its sidewalks receive every day. The results of this
study will be used to determine whether the city needs to fund more sidewalks.
The city has surveyed various buildings in several blocks to determine the traffic
patterns they generate. Your job is to take this survey data and convert it
into sidewalk utilization information.

Your program will read in the size of the map and a map of several city blocks.
Buildings, streets, and building entrance/exits will be marked on the map. You
will also be given a list of pedestrian load between several pairs of exits
and entrances. Your program will determine the paths used by pedestrians between
each source and destination, add up the total pedestrian load from all paths
using each street, and output a table of the total pedestrian load on each square.

Notes:

�� The map is divided into squares. Each square of the map can be a street square,
a building square, or an entrance/exit square. An entrance/exit square serves
as both entrance and exit for that building. There will be no more than 90 street
squares in the map.

�� People will always follow the shortest path between their origin and destination.
No shortest path will exceed 75 squares.

�� If there are multiple equal-length shortest paths, the load will be divided
equally amongst the paths. For shortest paths, there will be fewer than 50000
equallength path combinations.

�� If a building entrance/exit has multiple sides facing a street (for example,
a corner of a building), the pedestrians may enter or exit through any street-facing
side.

�� All movement will be strictly N, E, S, or W. No diagonal movement is permitted.

�� Pedestrians cannot move through buildings or off the edge of the map.

�� For convenience, you may ignore the fact that each street section may have
two sidewalks.

�� Traffic load is not applied to the actual exit/entrance squares themselves.

�� If an origin and destination are adjacent on the map, pedestrians may move
directly between them. In this case, there is no resulting load placed on any
portion of the map because no streets are used.

**Input format: **

Line 1: X Y

X is the number of columns in the map, Y is the number of rows. Each is a positive
integer less than 20.

Line 2-(Y+1):

Each line contains exactly X symbols indicating the contents of that square
on the map. The symbols are:

X: building, non-entrance/exit

.: (period) street

{A-O}: letter indicating exit/entrance. Each letter may occur at most once.

Lines (Y+2)-?:

Each line indicates a pedestrian route and specifies a source, destination,
and pedestrian load. Source and destination will each be a letter {A-O} with
no spaces in between. The load factor will be a nonnegative integer, separated
from the destination by whitespace. Source and destination will never be equal.
At most 25 routes will be given. There will be a valid path in the map for each
requested route.

The file will terminate with the line:

XX 0

**Output format: **

The output consists of Y lines, each with X space-separated fields indicating
the load factor. Each load factor is printed to two decimal places with 3 spaces
for integer digits (C 6.2 format).

Sample Input:

4 4

....

A.X.

XXX.

B...

AB 2

BA 1

XX 0

Sample Output:

1.50 3.00 3.00 3.00

0.00 1.50 0.00 3.00

0.00 0.00 0.00 3.00

0.00 3.00 3.00 3.00

Source:

**Mid-Atlantic USA 2001**
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