Protein are chains of molecules chosen (with repetition) from some 20 different amino acids. In a living cell, proteins are synthesized through the genetic code, a mechanism whereby ordered sequences of nucleotides in the messenger RNA dictate the formation of a particular amino acid. The four key nucleotides are adenine, quanine, cytosine, and uracil (A, G, C, and U). Assuming A, G, C, and U can appear any number of times in a nucleotide chain and that all sequences are physically possible, what is the minimum length the chains must attain to have the capability of encoding the entire set of amino acids? Note: Each sequence in the genetic code must have the same number of nucleotides.