A message of length x symbols is made from a set of 8 symbols drawn from a vocabulary shown below, with each symbol being coded using 3 binary bits: So, the message BADGE (x=5) would be coded as 001, 000, 011, 110,100. This message requires a constant 3 bits/symbol. Analysis shows that in general usage, the symbols appear with the relative frequency as shown also in the table. (i) Construct a Huffman coding tree to determine the most efficient alternative coding for the symbols so as to minimise the number of bits/symbol to code a message. (ii) Determine the average number of bits/symbol required to code a message using this more efficient alternative coding