Kelvin has a set of eight vertices. For each pair of distinct vertices, Kelvin independently draws an edge between them with probability p \in(0,1). A set S of four distinct vertices is called good if there exists an edge between v and w for all v, w \in S with v \neq w. The variance of the number of good sets can be expressed as a polynomial f(p) in the variable p. Find the sum of the absolute values of the coefficients of f(p).
(The variance of random variable X is definedas \mathbb{E} [X^2]−\mathbb{E}[X]^2.)