The Committee for Research on Binary Viruses discovered a method of replication for a large family of viruses whose genetic codes are sequences of zeros and ones. Each virus originates from a single gene; for simplicity genes are denoted by integers from (0) to (G - 1). At each moment in time a virus is a sequence of genes. When mutation occurs, one of the genes from the sequence is replaced by a certain sequence of genes, according to the mutation table. The virus stops mutating when it consists only of genes (0) and (1). For instance, for the following mutation table: () 2 \to \langle 0\ 1 \rangle \\ 3 \to \langle 2\ 0\ 0\rangle\\ 3 \to \langle 1\ 3\rangle\\ 4 \to \langle 0\ 3\ 1\ 2\rangle\\ 5 \to \langle 2\ 1\rangle\\ 5 \to \langle 5\rangle () a virus that initially consisted of a single gene (4), could have mutated as follows: () \langle 4 \rangle \to \langle \underline{0\ 3\ 1\ 2} \rangle \to \langle 0\ \underline{2\ 0\ 0}\ 1\ 2 \rangle \to \langle 0\ \underline{0\ 1}\ 0\ 0\ 1\ 2 \rangle \to \langle 0\ 0\ 1\ 0\ 0\ 1\ \underline{0\ 1} \rangle () or in another way: () \langle 4 \rangle \to \langle \underline{0\ 3\ 1\ 2} \rangle \to \langle 0\ \underline{1\ 3}\ 1\ 2 \rangle \to \langle 0\ 1\ 3\ 1\ \underline{0\ 1} \rangle \to \langle 0\ 1\ \underline{2\ 0\ 0}\ 1\ 0\ 1 \rangle \to \langle 0\ 1\ \underline{0\ 1}\ 0\ 0\ 1\ 0\ 1 \rangle () Viruses are detected by antibodies that identify the presence of specific continuous fragments of zeros and ones in the viruses' codes. For example, an antibody reacting to a fragment (\langle 0\ 0\ 1\ 0\ 0 \rangle) will detect a virus (\langle 0\ 0\ 1\ 0\ 0\ 1\ 0\ 1 \rangle), but it will not detect a virus (\langle 0\ 1\ 0\ 1\ 0\ 0\ 1\ 0\ 1 \rangle). For each gene from (2) to (G-1), the scientists are wondering whether a given set of antibodies is enough to detect all viruses that can emerge through mutations from this gene. If not, they want to know the leng