Chapter $7$ part $3($ch$07\mathrm{.}03$ Theorem Part $3$ RE to FA$)$ discusses the algorithm to construct the union of two machines. On page $4$ of the powerpoint pdf file $($ch$07\mathrm{.}03$ Theorem Part $3$ RE to FA$.$pdf$),$ it indicates that each new state in the union machine corresponds to some combination of $x-$states and $y-$states, where $x$ states represents the states from FA$1,y-$states represents the states from FA$2.$ In this problem, FA$1$ has $7$ states and FA$2$ has $6$ states, what is the maximum possible number of states in the union FA$1+$FA$2?($Note: your answer must be an integer value, such as $5)$