PROB7: GOPHER HOLE II

Be a gopher-hole player's assistant.

INPUT: prob7.dat

A sequence of player's views of gopher hole games, formatted as in the output of GOPHER HOLE I. The games are not necessarily successive nor even from the same field. None of the views will be after the player picked a hole. For example:

       column   111111111122222222223
       123456789012345678901234567890
line 1:+----------+[EOL]
     2:|###1      |[EOL]
     3:|#311      |[EOL]
     4:|11        |[EOL]
     5:|          |[EOL]
     6:|          |[EOL]
     7:|          |[EOL]
     8:|          |[EOL]
     9:|          |[EOL]
    10:|          |[EOL]
    11:|          |[EOL]
    12:+----------+[EOL]
    13:[EOL]
    14:+----------+[EOL]
    15:|##1       |[EOL]
    16:|#21       |[EOL]
    17:|11        |[EOL]
    18:|          |[EOL]
    19:|          |[EOL]
    20:|          |[EOL]
    21:|          |[EOL]
    22:|          |[EOL]
    23:|          |[EOL]
    24:|          |[EOL]
    25:+----------+[EOL]
    26:[EOF]

OUTPUT: prob7.out

A '*' is printed if it can be logically concluded that a hole is at this location.
A '$' is printed if it can be logically concluded that a hole is not at this location.
A '?' if no deterministic conclusion can be drawn about the existence of a hole at this location.

For the example input, this would be:

       column   111111111122222222223
       123456789012345678901234567890
line 1:Program 7 by team 0[EOL]
     2:+----------+[EOL]
     3:|*$*1      |[EOL]
     4:|*311      |[EOL]
     5:|11        |[EOL]
     6:|          |[EOL]
     7:|          |[EOL]
     8:|          |[EOL]
     9:|          |[EOL]
    10:|          |[EOL]
    11:|          |[EOL]
    12:|          |[EOL]
    13:+----------+[EOL]
    14:[EOL]
    15:+----------+[EOL]
    16:|$*1       |[EOL]
    17:|*21       |[EOL]
    18:|11        |[EOL]
    19:|          |[EOL]
    20:|          |[EOL]
    21:|          |[EOL]
    22:|          |[EOL]
    23:|          |[EOL]
    24:|          |[EOL]
    25:|          |[EOL]
    26:+----------+[EOL]
    27:End of program 7 by team 0[EOL]
[EOF]