FERMAT 2008 Problem 8

Two 3-digit integers, a b c and \operatorname{def}, have the following property:

\begin{array}{r} a b c \\ +\quad d e f \\ \hline 1000 \end{array}

None of a, b, c, d, e, or f is 0 . What is a+b+c+d+e+f ?

Answer Choices
A. 10
B. 19
C. 21
D. 28
E. 30