Assume that the current S&P 500 index value is 3,500 and a portfolio with a current value of $7,000,000 portfolio has a beta of 2.5. The portfolio manager want to use a S&P 500 index put option to protect the portfolio value to a level of $6,300,000 over the next six months (include dividends). Assume that all dividends are paid continuously, the annual dividend yield on the index is 3%, the annual dividend yield on the portfolio is 2%, and the annual risk free interest rate is 2% (continuously compounding). How many options should the manager buy? What is the strike price of the option?