In a two-period CRR model with = 1% per period, S(0) = 100, u = 1.02

In a two-period CRR model with τ = 1% per period, S(0) = 100, u = 1.02 and d = 0.98, consider an option that expires after two periods, and pays the value of the squared stock price, S2(t), if the stock price S(t) is higher than $100.00 when the option is exercised. Otherwise (when S(t) is less or equal to 100), the option pays zero. Find the price of the American version of this option.