Minimizing Sum Of Roots

Algebra Level 5

$\sqrt{x^2+4}+\sqrt{(x-2)^2+(y-2)^2}+\sqrt{4+(3-y)^2}$

Let $$x$$ and $$y$$ be real numbers. And Let $$s$$ be the minimum value of the above expression. Find the value of $$\lfloor 1000s\rfloor$$.

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