Let $I, T, E, S$ be distinct positive integers such that the product $ITEST = 2006$. What is the largest possible value of the sum $I + T + E + S + T + 2006$?

\[ \textbf{(A) } 2086 \quad \textbf{(B) } 4012 \quad \textbf{(C) } 2144 \]

Let's think step by step and output the final answer within \boxed{}.
user