We say that a polynomial p is \mathit{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 \mathit{disguising}~ if it is nonzero, and all of its non-zero coefficients lie between 0 and 1, exclusive. Determine \sum \text{deg}(f)\cdot f(2) over all disguising polynomials f of degree at most 5.