Suppose the U$.$S$.$ president wants to estimate the proportion of the population that supports his current policy toward revisions in the health care system. The president wants the margin of error to be $0\mathrm{.}05.$ Assume a $99\%$ level of confidence. The president$$s political advisors found a similar survey from two years ago that reported that $45\%$ of people supported health care revisions.

a$.$ How large of a sample is required? $($Round intermediate values to $2$ decimal points. Round your answer up to the next whole number.$)$

b$.$ How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? $($Round intermediate values to $2$ decimal points. Round your answer up to the next whole number.