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Build a huffman code for an alphabet with the following probabilities: a: 0.15, b: 0.05, c: 0.2, d: 0.01, e: 0.3, f: 0.06, g: 0.04, h: 0.07, i: 0.12. show the successive trees, stage by stage (including the starting stage with trivial trees), including the final tree. also, submit the resulting binary encodings for each letter.

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