Is it really Inequality Problem-2?

Let $p,q,a$ be real numbers such that $p^{2}+q^{2}-2p=0$ , then the minimum value of $\sqrt{p^{2}+q^{2}+2a^{2}+16-2ap-8a-8q+2aq}$ is $\frac{m}{\sqrt{e}}-d$ where $m,e$ are prime numbers and $d$ is a positive integer . Find $m+e+d$ .