For a large population of cash disbursement transactions, Smith, CPA is testing controls by using attribute sampling techniques. Anticipating an expected deviation rate of $3$ percent, Smith found from a table that the required sample size is $400$ with a tolerable deviation rate of $5$ percent and a desired confidence level of $95$ percent. If Smith anticipated an expected deviation rate of only $2$ percent but wanted to maintain the same tolerable deviation rate and confidence level, the sample size would be closest to