You have a set of 20 different objects.

Let $S$ be the total number of ways in which you can **select and permute** any number of these objects.

Find the digit sum of $S$.

**Details and Assumptions**

- The digit sum of a number is the sum of its individual digits. For example, the digit sum of 121 is $1+2+1 = 4$.
- You can pick any number of objects, from 0 to 20.

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