Vanya has to now choose some Students from her class to go to the International Mathematical Olympiad. She knows for each student of her class, $$3$$ pieces of information about them, i.e. their 'Name', 'Age' and 'Aptitude'.
Vanya, to make work easier for her, and more difficult for you, defines the Winning Quotient of the Students choosen for the Olympiad from her class to be the Summation of their Aptitude Levels. In short, assume Vanya chooses Students $$x$$, $$y$$ and $$z$$. She considers the Winning Quotient to be Aptitude Level(x) + Aptitude Level(y) +Aptitude Level(z) in case of such a selection.
Now, considering that Vanya randomly chooses any arbitrary subset of Students from her class to visit the Olympiad, where the size of this subset has to be at least $$1$$, and the probability of each subset being choosen is equal, Vanya wishes to know the Expected Value of the Winning Quotient of the choosen Students.
She finds this task rather challenging, and wants you to help her out. Can you do it ?
Table : Students
Round down your answer to 2 decimal places, and then select it to output.
Sample Students Table :
Input Constraints :
The input table shall consist of no more than 10 rows. The Aptitude level of each student shall lie in the range from $$1$$ to $$10$$ inclusive. The Name and ID of each Student shall consist of at least 1 and no more than 10 characters.