Consider the problem of determining the optimal merge order in external sorting by merge sort. Assume we have the following sorted runs and their respective lengths (#records) in parenthesis: R1(550), R2(320), R3(260), R4(810), R5(430), R6(770), R7(940). (a) Find the optimal merge order by using the Huffman Code method. (Draw the intermedia steps and the final Huffman tree.) (b) Assume that the cost of merging a record once is $5. What is the total cost of merging using the optimal order found in (a)? (Write the formula and compute the total cost.)