The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 20-inch pizzas. She takes a random sample of 30 pizzas and records their mean and standard deviation as 20.50 inches and 2.10 inches, respectively. She subsequently computes the 90% confidence interval of the mean size of all pizzas as [19.87, 21.13]. However, she finds this interval to be too broad to implement quality control and decides to reestimate the mean based on a bigger sample. Using the standard deviation estimate of 2.10 from her earlier analysis, how large a sample must she take if she wants the margin of error to be under 0.5 inch? (You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places and "z" value to 3 decimal places. Round up your answer to the nearest whole number.)