A company manages its inventory for a specific item using the periodic review inventory model with $4$ days between orders. It is currently time to place an order, and the company notes that there are $220$ items on hand. The item to be replenished has a lead time of $2$ days with a daily demand of $410$ units. The standard deviation of demand during the uncertainty period has been calculated to be $40.$ If the company wants to have at least a $99\%$ service level for this item, what should its order quantity be$?$

$$ Click the icon to view the table for the $z-$values for the given probabilities.

The order quantity is

units. $($Enter your response rounded up to the next whole number.$)$