The move to front technique is a pre-processing step that can be applied before Huffman or arithmetic coding. The idea is map the n characters of the source to numbers 0 . . . n 1 in a way which changes as the source is processed. Initially the mapping is arbitrary. Whenever a source character is coded, the mapping is changed so that that character maps to 0 and other characters are moved up to make room. More precisely if at some moment, aij maps to j for each j and we code aik then we change the map so that for each 0 j < k aij maps to j + 1, and aik now maps to 0. (a) Using this idea and the initial mapping e 0, m 1, n 2, o 3 and y 4, translate the string moneymoneymoney. (b) Compute the frequencies of the letters in the original message and of the numbers in the translated message, and the entropy of sources with those frequencies. (c) Explain why this pre-processing step could be helpful in compressing data such as natural language text