Consider a source with $5$ possible messages: a$1,$ a$2,$ a$3,$ a$4,$ a$5.$

Suppose this source generates its message according to the following probability distribution:

P$($a$1)=0$:$24$; P$($a$2)=0$:$22$; P$($a$3)=0$:$20$; P$($a$4)=0$:$18$; P$($a$5)=0$:$16$:

How many bits would a Huffman code assign to message a$3?$