Juno has realized that the hypothesis space H from Q$1\mathrm{.}3$ would be too large to model her taste.

She instead tries to evaluate each criterion by assigning numeric scores such as

$$ Food: poor $=-1,$ average $=0,$ good $=1$

$$ Ambiance: inferior $=-1,$ normal $=0,$ superior $=1$

$$ Service: bad $=-1,$ fair $=1$

Her goal is to restrict hypotheses to certain functions that only use the sum of any two attribute values for predicting her potential preference. In particular,

$$ Like $=$ yes if sum $>0$

$$ Like $=$ no if sum $<0.$

Under this restriction, for instance, Juno now likes the Restaurant $4$ in D because it achieves $2$ points from its good food and fair service despite its inferior ambiance.

Let H$\text{'}$ be the restricted hypothesis space $($HI C H$)$ that satisfies the above numeric prediction rule. Measure the size H$\text{'},$ a new restricted hypothesis space of H$.($Hint: Consider each of the three cases where only $\{$F$,$ A$\},\{$F$,$ S$\},$ or $\{$A$,$ S$\}$ matters and the other one attribute doesn't care. Make sure that Hi must be a subset of H$)$

$($Please only type in the final result number in format $"9"$ or $"3^2",$ without quotation marks, any other extra letters nor spaces, or the autograder won't work properly$).$