# How does changing input size affect The Goldreich-Goldwasser-Micali Construction?

If we want to construct a PRF that is length preserving, it is easy to show with hybrid proof that the resulting construction is a PRF.

But what happens when we have longer input. Supose that the key and output length are $$n$$ and the input size is $$2n$$.

I have been imagining what could happen to the binary tree. I feel like since input is double the size it will go double the depth. But in this case I cant tell if the resulting construction is a PRF.