$\begin{array}{ccccccc} & & \color{blue}{A} & \color{blue}{A} &\color{blue}{A} \\ & & \color{red}{B} & \color{red}{B} & \color{red}{B} \\ + & & \color{green}{C} & \color{green}{C} & \color{green}{C} \\ \hline & & D & D & D\\ \end {array}$

The above represents a cryptogram such that each letter represents a **distinct** single digit positive integer. Find the number of solutions to the above cryptogram.

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