Suppose we have a file containing only the characters a$,$ e$,$ i$,$ t$,$ h$,$ plus blank space and newline. Using

standard coding, $3$ bits is required in order to represent $7$ symbols. Assuming that the frequency of letters

in the file is:

Character Code Frequency Total Bits

a $0002060$

e $0013090$

i $0102575$

t $011824$

h $1001030$

space $1011648$

newline $11026$

$($a$)$ What is an optimal Huffman code for this file?