A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $$8\mathrm{.}50$ per stone for quantities of $600$ stones or more, $$8\mathrm{.}90$ per stone for orders of $400$ to $599$ stones, and $$9\mathrm{.}40$ per stone for lesser quantities. The jewelry firm operates $104$ days per year. Usage rate is $22$ stones per day, and ordering costs are $$42.$

a$.$ If carrying costs are $$2$ per year for each stone, find the order quantity that will minimize total annual cost. $($Do not round intermediate calculations. Round your final answer to the nearest whole number.$)$