Consider a g$-$base numeral system, where g is $($the length of your last name $+$ the length of your first name$)/3$ rounded to the nearest integer. Recall that in the g$-$base system the alphabet of the digits is $\backslash$Sigma g $=\{0,1,2,...,$ g $1\}.$ Construct a DFA $($Deterministic Finite Automaton$)$ A$1=\{$Q$1,\backslash$Sigma g$,\backslash$delta $1,$ s$1,$ F$1\}$ that checks if the input written in the g$-$base numeral system can be divided by g $1.$ A number is divisible by g $1$ in the g$-$base numeral system, if the sum of its digits is divisible by g $1.$ Hint $1$ use modular addition. Also provide the graphs with corresponding nodes and edges by clearly indicating weights and directions. Be as precise as possible and give a very detailed explanation. Useful: E$.$ Kinber, C$.$ Smith. "Theory of Computing: A Gentle Introduction", $2000-$ Chapter $2.$ Finite Automata

section $2\mathrm{.}1($example $2\mathrm{.}1\mathrm{.}3),$ pages $16-17$