The admissions office of a college wants to estimate the mean SAT math score for their entering class next year. Because they don't know yet exactly who will be in the class, they want to take a sample of those who have already been admitted and have indicated they will definitely attend. If we use the standard deviation σ = 100, how many students will they need to sample to estimate the true mean to within 25 points at 99% confidence? The z for a 99% confidence interval is _____.