Compound A has the formula $\mathrm{C}_{10} \mathrm{H}_{16}$. On catalytic hydrogenation over palladium, it reacts with only 1 molar equivalent of $\mathrm{H}_{2}$. Compound A also undergoes reaction with ozone, followed by zinc treatment, to yield a symmetrical diketone, $\mathbf{B}\left(\mathbf{C}_{10} \mathrm{H}_{16} \mathrm{O}_{2}\right)$
(a) How many rings does A have?
(b) What are the structures of A and B?
(c) Write the reactions.