Let $ \mathbb{R} $ denote the set of all real numbers. Let $ f: \mathbb{R} \to \mathbb{R} $ be a function such that $ f(x)>0 $ for all $ x \in \mathbb{R} $, and $ f(x + y) = f(x)f(y) $ for all $ x, y \in \mathbb{R} $.
Let the real numbers $ a_1, a_2, \ldots, a_{50} $ be in an arithmetic progression. If $ f(a_{31}) = 64f(a_{25}) $, and
$$
\sum_{i=1}^{50} f(a_i) = 3(2^{25} + 1),
$$
then the value of
$$
\sum_{i=6}^{30} f(a_i)
$$
is __________.