Let $x=2$ be a root of the equation $x^{2}+px+q=0$ and define \[ f(x)= \begin{cases} \dfrac{1-\cos\!\big(x^{2}-4px+q^{2}+8q+16\big)}{(x-2p)^{4}}, & x\ne 2p,\\[6pt] 0, & x=2p. \end{cases} \] Then $\displaystyle \lim_{x\to 2p^{+}} \big[\,f(x)\,\big]$, where $[\cdot]$ denotes the greatest integer function, is: