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$\large{\begin{array}{ccccccc} && & & & & A&A\\ && & & & & B&B\\ +&& & & & & C&C\\ \hline & & & & & A & B&C\\ \end{array}}$

If each of $A,B,C$ represents a distinct digit from 1 to 9, then what is the value of $\overline{ABC}?$

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