For $f(x) \in Z[x]$, polynomials with integer coefficients, we define the “symbolic derivative”, $f'(x)$ of $f(x)$. For constant functions $f(x) = c$ we define $f'(x) = 0$ and if $f(x) = a_0 + a_1x + a_2x^2 + ...+ a_nx^n$ then we define $f'(x) = a_1 +2a_2x+...+na_nx^{n-1}$. Further, for $f(x) = a_0 +a_1x+...+a_nx^n$ we define a function $h : Z[x] \to N$ by $h(f(x)) = \sum^{n}_{i=0}|a_i|$, which we call the height of $f(x)$. If the number of polynomials $f(x)$ with integer coefficients satisfying $f'(f(x))f'(x) = 4xf(x)$ and $h(f(x)) < 23$ is $n$, enter $n$.