AMC 12 2007a Problem 22

For each positive integer $n$, let $S(n)$ denote the sum of the digits of $n.$ For how many values of $n$ is $n + S(n) + S(S(n)) = 2007?$

$\mathrm{(A)}\ 1 \mathrm{(B)}\ 2 \mathrm{(C)}\ 3 \mathrm{(D)}\ 4 \mathrm{(E)}\ 5$