# Is it really Inequality Problem-2?

Algebra Level 5

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 $$m+e+d$$.

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