If $\phi$ is the Golden Ratio, we know that $\frac{1}{\phi} = \phi - 1$. Define a new positive real number, called $\phi_d$, where $\frac{1}{\phi_d} = \phi_d - d$ (so $\phi = \phi_1$). Given that $\phi_{2009} = \frac{a + \sqrt{b}}{c}$, where $a$, $b$, $c$ are positive integers, and the greatest common divisor of $a$ and $c$ is 1, find $a + b + c$.

Let's think step by step and output the final answer within \boxed{}.
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