The Mysterious Number

Each letter in the following cryptogram represents a distinct, non-zero digit: ABCDEF×3BCDEFA.\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?A+B+C+D+E+F?

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