Suppose you have a message that contains only the following seven letters, with the listed

frequency counts:

Build the Huffman tree for these characters. Remember that when you label the branches,

put the $0$ on the branch that connects to the smaller number. Prove that you got the right

tree by decoding the following English word $($if you get gibberish, you did something wrong!$)$:

$0111101010001111011$

Type in the word using only lower$-$case letters.