You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99.9% confident that you...

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99.9% confident that you estimate is within 1% of the true population proportion. How large of a sample size is required?

n
= ?

Do not round mid-calculation. However, use a critical value accurate to three decimal places.