# Not a Typo 2

Algebra Level 4

Real numbers $$a,b,c$$ are such that $$ab+bc+ca=1$$ and the maximum value of $$\frac{1}{1+a^2}+\frac{1}{1+b^2}+\frac{6c}{1+c^2}$$ is $$m+\frac{p\sqrt{q}}{r}$$, where $$m,p,q,r$$ are all positive integers with $$\gcd(p,r)=1$$ and $$q$$ square free. Find the value of $$m+p+q+r$$.

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