You are managing a portfolio of large$-$cap stocks and you are concerned about a potential market downturn. The portfolio has a market value of $$5$ million and you want to hedge against potential losses using S&P $500$ futures contracts. The current S&P $500$ index is $4,000$ and each futures contract represents $250$ units of the index. The margin requirement for each contract is $$15,000$ and the futures price is $$4,020.$ How many futures contracts do you need to purchase to effectively hedge against a market downturn?