A regional distributor for a major electronics company forecasts sales of $20,000$ LCD screens of a specific model for the next year. The annual carrying cost per screen is $$25,$ and the ordering cost for each batch is $$200.$ The distributor is open $300$ days per year. What is the Economic Order Quantity $($EOQ$)?($round up the answer$)$

$300$ screens

$566$ screens

$1200$ screens

$1600$ screens