Problem $3$: $(15$ points$)$ Suppose the symbols $a,c,d,e,l,m,n,o$ occur with frequencies $12/64,$

$\frac{9}{64},\frac{6}{64},\frac{14}{64},\frac{5}{64},\frac{4}{64},\frac{3}{64},\frac{11}{64}$ respectively in a file consisting of $9600$ characters.

$(10$ points$)$ What is the Huffman encoding of the alphabet? $($your work should show

the process of building a Huffman tree and giving the final encoding.$)$

$(5$ points$)$ What is the total length of the encoded file in bits?