For all positive integers \(x\), let \[f(x)=\begin{cases}1 &\mbox{if x = 1}\\ \frac x{10} &\mbox{if x is divisible by 10}\\ x+1 &\mbox{otherwise}\end{cases}\] and define a sequence as follows: \(x_1=x\) and \(x_{n+1}=f(x_n)\) 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 \(m\).

(第二十二届AIME1 2004 第15题)