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For a function \(f : [\![1, n]\!] \to \{1995, 1996\}\), define:
$$F_f(n) = f(1) + f(2) + \cdots + f(n)$$
And define \(G(n)\) to be the number of functions \(f\) such that \(F_f(n)\) is even. Find \(G(10^9) \pmod {1\; 000 \; 000 \; 007}\)
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