AMC 12 2014a Problem 15

A five-digit palindrome is a positive integer with respective digits $abcba$, where $a$ is non-zero. Let $S$ be the sum of all five-digit palindromes. What is the sum of the digits of $S$?

$\textbf{(A) }9 \textbf{(B) }18 \textbf{(C) }27 \textbf{(D) }36 \textbf{(E) }45$