Time Limit: 10 Seconds
Memory Limit: 32768 KB
In World War II, Germany once used an electronic encryption machine called
Enigma, which played a decisive role in the initial victories of Nazi Germany.
It was proved to be one of the most reliable encryption systems in history.
However, it was the blind trust on the reliability of the machine that brought
about the doom of its user.
The structure of a one-rotor Enigma is shown as follows (the Enigma has only
The key element of the Enigma is the rotor, as shown in the second figure,
which uses electronic circuits to transform plaintext (input from keyboard)
into cryptograph (output on screen). When one key on the keyboard is pressed,
the corresponding cryptograph is shown on screen. Then the rotor will automatically
revolve a one-letter-step to a different position. The following figures illustrate
how the rotor works when letter "b" is pressed three successively
When letter "b" is pressed for the first time, the signal goes through
the circuit and "A" is shown on screen. When the key is released,
the rotor revolves one-letter-step to a different position that changes all
the corresponding circuits so that each letter now has a different cryptograph.
When letter "b" is pressed for the second time, the corresponding
cryptograph is "C". So when letter "b" is pressed for the
third time, the cryptograph is "E" according to the principle specified
Now the following figure shows the structure of a two-rotor Enigma.
The difference is that when a key is released, the second rotor won't revolve
a step until the first one has finished one circle and returns to the original
position. This is also the same in the case of three-rotor Enigma. That is:
Only after the first rotor has finished one circle and return to the initial
status, the second rotor will revolve a step. And only after the second rotor
has finish one circle, the third rotor will revolve a step.
However, how did the Allied Forces obtain the information encrypted by Enigma?
A person named Hans-Thilo Schimdt was very essential. He acted as a spy and
provided the initial status of the three rotors in each Enigma to the Allied
Forces once a month. The Allied Forces thus got everything they wanted by deciphering
the intercepted cryptograph using the information offered by the spy.
Now, please design a program to obtain the plaintexts using the information
offered by the Allied Forces.
The input file contains several test cases representing several three-rotor
Enigmas. The last test case in the input file is followed by a line containing
a number 0.
Each case begins with a line containing an integer m (1 <= m <= 26) which indicates
the number of sequential letters each rotor has. The first letter will always
be A. (for example, m = 6 tells each rotor has 6 keys from A to F). The following
three lines describe the initial status of the three rotors respectively. Each
of them contains a string consisting of m capital character. For instance, a
rotor with the initial status "BADFEC" indicates that the initial
encrypt mechanism is to convert "abcdef" to "BADFEC", that
is, original letter "a" corresponding to cryptograph letter "B",
"b" to "A", "c" to "D", "d"
to "F", "e" to "E" and "f" to "C".
The forth line of each case contains an integer n which tells the number of
cryptographs generated by the above Enigma. Then the following n lines are the
n cryptographs respectively, which consist of m capital characters each.
For each test case, the output should consist of two parts. The first line is
the number of Enigma and a colon. The following lines are the plaintexts deciphered
from the corresponding cryptographs. Each plaintext should be printed in one
line. Note: The characters in the plaintext should be converted to the corresponding
lowercases before they are printed.
Insert a blank line between test cases.
Output for the Sample Input
Source: Asia 2001, Shanghai (Mainland China)