Logical Solutions

$\begin{array}{ccccccc} & & \color{#3D99F6}{A} & \color{#3D99F6}{A} &\color{#3D99F6}{A} \\ & & \color{#D61F06}{B} & \color{#D61F06}{B} & \color{#D61F06}{B} \\ + & & \color{#20A900}{C} & \color{#20A900}{C} & \color{#20A900}{C} \\ \hline & & D & D & D\\ \end {array}$

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.