**The "Bounded" Automata**

- Unlike the automata in "A New Kind of Science", the automata for this problem operate in a "bounded space". In other words, each line output by an automaton consists of exactly n squares, and, the first square, and the last square of the output from a bounded automaton are always white no matter what the rule for the automata. This means that while an automaton can examine the first and last square of its input line when computing the new second and second to last characters, it cannot change the first or last square when it outputs a line. Thus, the first and the last square on a line must always remain white.
- Bounded automata will always start life on a line with an odd number of squares, and all of the squares (except the middle square) are white. The middle square for step 1 is always black.
- The number of squares is determined by the string for which the program is searching (the second field of an input line)

**The Program**For every line in the input, your program must determine which (if any) of the 255 possible automata could have generated that particular line when started from the standard starting state. If none of the automata generate the sequence by the given step number, output "NONE". If more than one automata generated that line, then, you must output all of the automata that generate the line as described below in the output section.