$2.$ Now Double It Again $[10$ points$]$

Give a state diagram for the Turing Machine you described in question $(1),$ for the language

L $=\{$w in $\{$a$,$ b$,$ c$\}$

$$

: the number of a$$s in w is more than twice the number of b$$s$\}$

You may $($but do not have to$)$ omit the reject state, under the assumption that if a transition for a tape character is

not present on a given state, it transitions to the reject state. If you do include the reject state, you are expected to

explicitly indicate all transitions to it$.$ You should use to indicate a blank tape square, and you may assume that

is the symbol on the tape squares immediately preceding and immediately following the first and last tape squares with

input symbols, respectively.

Your state diagram for this question may be handwritten.