You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of $25$ bacteria reveals a sample mean of $\stackrel{}{x}=80$ hours with a standard deviation of $s=7$ hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of $0\mathrm{.}6$ hours at a $99\%$ level of confidence.

What sample size should you gather to achieve a $0\mathrm{.}6$ hour margin of error? Round your answer up to the nearest whole number.

$n=$

bacteria