Mastermind is a game played with a supply of pegs of various colours, or in the absence
of proper equipment, pen and paper (or a computer!) using letters A, B, C, etc, as ¡®pegs¡¯
with the different letters representing different colours. One player chooses some particular
arrangement of coloured pegs or letters and keeps it hidden. The other players attempts
to guess the arrangement, guided by a score that the first player determines for each guess.
In ordinary Mastermind, the score is in two parts: a ¡®black score¡¯ counting the number
of pegs that match the target peg in the same position, and a ¡®white score¡¯ that is the
number of pegs that are not themselves ¡®black¡¯, but match the colour of an otherwise
unmatched target peg in a different position from the guess peg.
Adjacent Mastermind adds a ¡®grey score¡¯ that is the number of pegs that do not match
their corresponding target pegs but can be matched up with otherwise unmatched target
pegs in the positions immediately to their left or right. (The leftmost and rightmost guess
pegs of course only have one slot that is adjacent to them and that might make them
grey.) The white score then becomes the number of pegs that are not themselves ¡®black¡¯
or ¡®grey¡¯, but match an otherwise unmatched target peg that is at least two positions
away from the guess peg.
As in ordinary Mastermind, each target peg may only be matched by at most one guess
peg, and each guess peg may only contribute to one of the scores at most once.
For example:

In guess 1, only the A in slot 1 contributes to the score, since only one peg may match the
target A and this one is the best match. Similarly in guess 3 only the B in slot 3 scores,
and similarly only one of the Cs in guess 4 scores. Finally in guess 5, only one of the As
counts as white, because there is only one target A available.
Adjacent Mastermind is theoretically easier for the guessing player because more information
is provided in response to each guess, but more difficult for the first player because
the scoring is more complicated. Your task is to help the first player by calculating each
guess¡¯s score.


Input consists of lines containing a target arrangement and a guess arrangement, separated
by a single space. Each arrangement is a string of between 2 and 50 uppercase letters,
¡®A¡¯ to ¡®Z¡¯. On each line, the guess arrangement will be of the same length as its target.
A single ¡®#¡¯ on a line by itself indicates the end of input. This line should not be processed.


Output will be one line for each target/guess input line, containing the guess and its score
in the format ¡®guess: b black, g grey, w white¡¯.

Sample Input


Sample Output

AAAA: 1 black, 0 grey, 0 white
ACEB: 1 black, 1 grey, 1 white
EFBB: 0 black, 1 grey, 0 white
ACBC: 1 black, 2 grey, 0 white
BEAA: 0 black, 1 grey, 1 white
ABCD: 4 black, 0 grey, 0 white
BCBCAA: 2 black, 2 grey, 0 white


New Zealand Programming Contest 2006