An option on a base stock without dividends, which expires in two months, has a return function of max (St^2 - 144.0), a risk-free interest rate of 4% (continuously compounded), and an annual volatility of the stock price of 20 %, the current price is 12 yuan.

(1) If the option is European, try to price it by constructing a two-period binary tree (one period is one month).

(2) If the above options are American, should the price be less?

1. ,,max(S- 144,0),4%(),20%, 12 (1),() (10) (2),?(5) 1. ,,max(S- 144,0),4%(),20%, 12 (1),() (10) (2)