Use the binomial tree analysis to value a $6-$month American put option with a $$65$ strike price on Crookshanks Corporation. The shares are currently trading for $$60.$ The annualized continuously compounded risk$-$free rate is $3\%.$ The volatility of the stock is $57\%.$ You will use the Cox Ross Rubenstein method for computing the binomial tree, and use a time step of $2$ months.