Statement

Edoardo found a very old typewriter that is undoubtedly fashionable, but not particularly efficient. In particular, when you type a string, the following errors may (randomly) happen: (1) Stuck key: when you type the same character two times consecutively (e.g. "aa"), only one of them is written (e.g. obtaining "a"). (2) Wild key: when you type a character (e.g. "a"), it may be repeated twice (e.g. obtaining "aa"). Furthermore, these errors may happen multiple times for the same string, and even multiple times for the same characters: for instance, a doubly stuck key would change "aaa" into "a" and a doubly wild key would do the opposite change. Before the first round, Edoardo wrote the password of the contest server three times with the typewriter, obtaining strings S_1, S_2, S_3. Edoardo does not remember the password any more and thus he needs to reconstruct it from these strings...