If the letters \(A\) to \(I\) represent distinct single digit positive integers with \(C = 3, G=7 ,I = 9\), find the values of each of these letters such that the grid above makes sense. Submit your answer as the 9-digit number, \(\overline{ABCDEFGHI} \).
###### Puzzle that inspired this problem.

**Details and Assumptions**:

The equation is evaluated from left to right, and BODMAS

**does not**apply.As an explicit example, If you think that \(\color{blue}1+13\times\color{blue}2\div\color{blue}3+\color{blue}4+12\times\color{blue}5-\color{blue}6-\color{blue}11+\color{blue}7\times\color{blue}8\div\color{blue}9-10 = 66 \) is true, then submit your answer as 123456789. (Note that the left hand side should evaluate to \( \frac{2530}{27} \)).

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