Refer to the Huffman Tree below for the following parts (a)-(c). Note that we follow the convention where the smaller frequency subtree would go on the right, and the larger on the left. You do not need to show work for this problem, but justifications may be considered for partial credit if you are incorrect. (a) (4 points) Decode the following messages using the above Huffman Tree, and do not use spaces. Ignore any boldface or underlining in the strings; they do not affect the decoding of the messages: i. 1110110101101000111011010011100101 ii. 100111010111100101100110 (b) (4 points) Suppose that we instead use a fixed length encoding to encode these messages, using the minimum number of bits required to encode these 9 characters. In which case: i. How many bits would be required to encode the message from 2ai? Which of the encodings between 2 ai and 2bi would require fewer bits? ii. How many bits would be required to encode the message from 2aii? Which of the encodings between 2aii and 2bii would require fewer bits? (c) (4 points) Complete the following frequency tables below that would correspond to the above Huffman Tree. You will receive full points if your frequency table results in the above Huffman Tree when using the Huffman building algorithm. Assume that no ties occur at any point in the algorithm, and that no letter's frequency exceeds 100. (d) (4 points) Use the Huffman Tree building algorithm to draw a Huffman Tree corresponding to the frequency table below