A stock price is currently $80.$ Over each of the next two $3-$month periods, it is expected to go up by $10\%$

or down by $10\%.$ The risk$-$free rate is $6\%$ per annum. Using a binomial tree, find the value of a $6-$month

American Put with strike $85$ if the stock is expected to pay a $$2$ dividend in $3$ months.