We say that a polynomial $p$ is respectful if $\forall x, y \in \mathbb{Z}$, $y - x$ divides $p(y) - p(x)$, and $\forall x \in \mathbb{Z}$, $p(x)  \in \mathbb{Z}$. We say that a respectful polynomial is disguising if it is nonzero, and all of its non-zero coefficients lie between $0$ and $1$, exclusive. Determine $\sum \deg(f)\cdot  f(2)$, where the sum includes all disguising polynomials $f$ of degree at most $5$.

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