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

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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