Three baskets and some balls are given to you. You are supposed to put these balls into these baskets by writing some positive numbers on the balls. But:
- The numbers you are supposed to write on them have to be positive integer number,
- In each basket, the numbered balls have to be distinct. (That also means you can put the same number in different baskets actually.)
- The sum of the numbers on the balls in all baskets has to be at most $31$.
- You do not have to put balls in every basket.
What is the maximum value of the multiplication of the numbers written on the balls?