Each letter in the following cryptogram represents a distinct, non-zero digit:
$\begin{array}{ccccccc}
& A & B & C & D & E & F \\
\times & & & & & & 3 \\
\hline
& B & C & D & E & F & A.
\end{array}$
What is $A+B+C+D+E+F?$

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