Do you know your ABCD's?

Logic Level 2

\[ \large{\begin{array}{cccccc} &A &B & C &D & E & F \\ \times & & & & &&F\\ \hline &G & G & G & G & G & G \\ \end{array}} \]

Given that \(A,B,C,D,E,F\) and \(G\) are distinct digits that satisfy the cryptogram above, find the value of \(A+B+C+D+E+F+G.\)

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