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Challenge 265: Digital Roots

To calculate the digital root of a number, you repeatedly sum its digits (which we will call the digit sum of a number) until you get down to a single digit number.

For example, to calculate the digital root of 374, we first calculate:

3 + 7 + 4 = 14

This is not a single digit number, so we will sum its digits again:

1 + 4 = 5.

5 is a single digit number, so we will stop there. In this case, the process of calculating the digital root took two steps.

What is the smallest number that requires five steps to calculate its digital root?

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