For some years, quite a lot of work has been put into listening to electromagnetic radio sig-nals
received from space, in order to understand what civilizations in distant galaxies might
be trying to tell us. One signal source that has been of particular interest to the scientists at
Universit´ e de Technologie Spatiale is the Nebula Stupidicus.

Recently, it was discovered that if each message is assumed to be transmitted as a se-quence
of integers a₀, a₁,...,a_n-1 the function

always evaluates to
values 0 ≤ f(k) ≤ 26 for 1 ≤ k ≤ n, provided that the correct value of p is used. n is of course
the length of the transmitted message, and the a_i denote integers such that 0 ≤ a_i < p. p is a
prime number that is guaranteed to be larger than n as well as larger than 26. It is, however,
known to never exceed 30 000.

These relationships altogether have been considered too peculiar for being pure coincidences,
which calls for further investigation.

The linguists at the faculty of Langues et Cultures Extraterrestres transcribe these messages
to strings in the English alphabet to make the messages easier to handle while trying to
interpret their meanings. The transcription procedure simply assigns the letters a..z to the
values 1..26 that f(k) might evaluate to, such that 1 = a, 2 = b etc. The value 0 is transcribed
to ’*’ (an asterisk). While transcribing messages, the linguists simply loop from k = 1 ton,
and append the character corresponding to the value of f(k) at the end of the string.

The backward transcription procedure, has however, turned out to be too complex for the
linguists to handle by themselves. You are therefore assigned the task of writing a program
that converts a set of strings to their corresponding Extra Terrestial number sequences.