(a) Deduce the structure of product A, which is highly symmetrical:
(FIGURE CAN'T COPY)
The following are selected spectral data for $\mathbf{A}$ :
MS $(m / z): 220\left(\mathrm{M}^{\dagger}\right)$
IR $\left(\mathrm{cm}^{-1}\right): 2930,2860,1715$
$$\begin{aligned}
&\left.^{1} \mathrm{H} \mathrm{NMR}(\mathscr{S}): 1.25(\mathrm{m}), 1.29(\mathrm{m}), 1.76(\mathrm{m}), 1.77(\mathrm{m}), 2.14(\mathrm{s}), \text { and } 2.22(\mathrm{t}) ; \text { (area ratios } 2: 1: 2: 1: 2: 2, \text { respectively }\right)\\
&^{13} \mathrm{C} \mathrm{NMR}(\delta): 23\left(\mathrm{CH}_{2}\right), 26\left(\mathrm{CH}_{2}\right), 27\left(\mathrm{CH}_{2}\right), 29(\mathrm{C}), 39(\mathrm{CH}), 41\left(\mathrm{CH}_{2}\right), 46\left(\mathrm{CH}_{2}\right), 208(\mathrm{C})
\end{aligned}$$
(b) Write a mechanism that explains the formation of A.