P4762 [CERC2014] Virus synthesis

Viruses are usually bad for your health. How about fighting them with... other viruses? In this problem, you need to find out how to synthesize such good viruses. We have prepared for you a set of strings of the letters $A, G, T$ and $C$. They correspond to the DNA nucleotide sequences of viruses that we want to synthesize, using the following operations: - Adding a nucleotide either to the beginning or the end of the existing sequence. - Replicating the sequence, reversing the copied piece, and gluing it either to the beginning or to the end of the original (so that e.g., $AGTC$ can become $AGTCCTGA$ or $CTGAAGTC$). We’re concerned about efficiency, since we have very many such sequences, some of them very long. Find a way to synthesize them in a minimum number of operations.

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