2、Lin Lin filled a cup with pure milk, the first time he drank $\frac{1}{3}$, then added soy milk, filled the cup and stirred evenly, the second time, Lin drank $\frac{1}{3}$ again, continued to fill the cup with soy milk and stirred evenly, repeated the above process, after the fourth time, Lin Lin drank a total of $\qquad$ (expressed as a fraction) of the total amount of pure milk.
$\frac{65}{81}$