In coding theory, unprefixed codes are often used as sets of words, none of which is a prefix. The word α is said to prefix the word β if α is obtained from β by deleting zero or more characters in end. For example, the words a, ab and aba are prefixes of the word aba. For example, the set of words aba, aa and bac is an unprefixed code, while the set of abac, aba< /code>, ba is not present because the word aba is a prefix of the word abac.
Professor Decipher works in the Useless Information Research Lab and studies his new invention of near-prefix codes. A set of words is called an almost prefix-free code of level k if the greatest common prefix of any two words from the set does not exceed k in length. For example, the set abac, abc, ba is a nearly unprefixed level 2 code, and the set abac, abab, ba do not exist because the longest common prefix of abac and abab is 3.
The next task that Professor Decifro set for his laboratory assistants is as follows: given a set of words and a number k, it is required to choose from the given words the maximum set, which is almost prefix-free level code k. You, as a junior laboratory assistant, were assigned to write the corresponding program.