As simple as ABC

\[ \begin{array} { l l l l l } & & & & & 9 & 9 & 9 \\ \times & & & & & A & B & C \\ \hline & & D & E & F & 1 & 3 & 2 \\ \end{array} \]

In this cryptogram, \(A,B,C,D,E\) and \(F\) are (not necessarily distinct) single digits. What is the value of \(A+B+C+D+E+F?\)

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