For all positive integers x, let
f(x)= \begin{cases}1 & \text { if } x=1 \\ x / 10 & \text { if } x \text { is divisible by } 10 \\ x+1 & \text { otherwise }\end{cases}
and define a sequence as follows: x_{1}=x and x_{n+1}=f\left(x_{n}\right) for all positive integers n. Let d(x) be the smallest n such that x_{n}=1. (For example, d(100)= 3 and d(87)=7.) Let m be the number of positive integers x such that d(x)= 20. Find the sum of the distinct prime factors of m.