Consider an unknown array $A$. We only know the following information about $A$:

1. It contains $6154$ integers
2. Its minimum value is equal to $9647$
3. Its maximum value is equal to $78417$

Consider the set of numbers $S$, containing all possible sums of the array $A$. A set is defined to only contain distinct elements, any repetition of elements will be ignored.

What is the total sum of all the elements of $S$?